Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atomPascal Szriftgiser1 and Edgardo S. Cheb-Terrab2 (1) University of Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers, Atomes et Mol\303\251cules, F-59000 Lille, France(2) Maplesoft, CanadaJSFHAbstractPauli first noticed the hidden SO(4) symmetry for the hydrogen atom in the early stages of quantum mechanics [1]. Starting from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states without explicitly solving Schr\303\266dinger's equation [2], [3]. In this paper, we derive that SO(4) symmetry and spectrum using a computer algebra system (CAS). While this problem is well known [4], [5], its solution involves several steps of manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein's sum rule for repeated indices. Therefore, it is an excellent model to test the current status of CAS concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. Generally speaking, when capable, CAS can significantly help with manipulations that, like non-commutative tensor calculus subject to algebra rules, are tedious, time-consuming and error-prone. The presentation also shows two alternative patterns of computer algebra steps that can be used for systematically tackling more complicated symbolic problems of this kind.<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>In this work we derive, step-by-step, the SO(4) symmetry of the hydrogen atom and its spectrum using a computer algebra system (CAS). To the best of our knowledge, such a derivation using symbolic computation has not been shown before. The goal was to see whether this computation can be performed entering only the main definition formulas, followed by only simplification commands, and without using previous knowledge of the result. The presentation that follows showcases that approach, illustrating different techniques. The intricacy of this problem is in the symbolic manipulation and simplification of expressions involving noncommutative quantum tensor operators. The simplifications need to take into account commutator rules, symmetries under permutation of indices of tensorial subexpressions, and use Einstein's sum rule for repeated indices.We performed the derivation using the Maple 2020 CAS with the Maplesoft Physics Updates v.913. Generally speaking, the default computational domains of CAS don't include tensors, noncommutative operators and related simplifications. The main exception is the Maple system, distributed with a Physics package that extends the default domain to include those objects and related operations. Physics redefines the multiplication and differentiation operators, so that they work with noncommutative and tensorial objects, including handling a new class, operators, that can have specific properties (Hermitian, Unitary, differential, etc.). Relevant for our purpose Physics includes a Simplify command which takes into account custom algebra rules, tensor symmetries, the sum rule for repeated indices, and uses tensor-simplification algorithms [6] adapted to work on a noncommutative domain. It is worth mentioning that other CAS have some tensorial and noncommutative capabilities, albeit limited. For example, Maxima includes the packages ctensor (to compute with tensor components) and atensor (to simplify a noncommutative dot product of tensors). However, to mention but one thing, the algebra rules are not customizable. It is not presently possible to define noncommutative Hermitian - possibly tensorial - operators, like position and momentum, and their commutator rules. Mathematica does not include packages like Physics or similar, but it includes basic noncommutative capabilities and some Tensor constructs. That functionality has been extended to some point by Mathematica users who developed tensor packages. However, to our knowledge, the combination of those capabilities and packages does not cover the requirements for problems like the one discussed here. E.g. it is not possible to express the starting point, the commutation rules between position, linear and angular momentum, noncommutative tensor operators, in simple terms as we do in equation in Sec. 2, nor to perform the simplifications of intermediate expressions performed in the following sections.A few notes about notation: when working with a CAS, besides the expectation of achieving a correct result for a complicated symbolic calculation, readability is also an issue. It is desired that one be able to enter the definition formulas and computational steps to be performed (the input, shown in what follows preceded by a prompt LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiPkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRUYvRjI=) in a way that resembles as closely as possible their paper and pencil representation, and that the results (the output, computed by the CAS) use easy-to-read, textbook mathematical-physics notation. The Maple Physics package implements such dedicated typesetting. In what follows, within text and in the output, noncommutative objects are displayed using a different color, e.g. LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRic=, vectors and tensor indices are displayed in the standard way, as in 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 and LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEicUYnRi9GNUY4Rj5GQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn, and commutators are displayed with a minus subscript, e.g. 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. Although the Maple system optionally provides dedicated typesetting also for the input, we preferred to keep visible the Maple input syntax, allowing for comparison with paper and pencil notation and to transmit a more accurate picture of what it is like to work on a real problem using CAS. We collected the names of the handful of commands used together with a one line description for them in an Appendix at the end. Maple also implements the concept of inert representations of computations, which are activated only when desired. We use this feature in several places. Inert computations are entered by preceding the command with % and are displayed in grey. Finally, as is usual in CAS, every output has an equation label, which we use throughout the presentation to refer to previous intermediate results, both in text and in input lines.In Sec.1, we present the standard formulation of the problem and the computational goal, which is the derivation of the formulas representing the SO(4) symmetry and related spectrum.In Sec.2, we formulate the problem on a Maple worksheet by setting tensorial non-commutative operators representing position, linear and angular momentum, respectively LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEiYUYnRi9GNUY4Rj5GQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn, LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictSSVtcm93R0YkNiYtRiw2KFEiYUYnRi9GNUY4Rj5GQUYvRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiM2Ji1GLzYoUSJhRidGMkY4RjtGPkZBRjJGOEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOC9GPFEnbm9ybWFsRic=, their commutation rules used as departure point, and the form of the quantum Hamiltonian LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2I1EhRidGNS9GOVEnbm9ybWFsRic=. That formulation is also used to derive a few related identities used in the sections that follow. In Sec.3, we derive the conservation of both angular momentum and the Runge-Lenz quantum operator, respectively 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 and 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. Taking advantage of the differentialoperators feature of the Physics package, we explore two equivalent approaches: first, using only a symbolic tensor representation LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEiakYnRi9GNUY4RjtGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn of the momentum operator; second, using an explicit differential operator representation for it in configuration space, 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. With the first approach, expressions are simplified only using the departing commutation rules, symmetries under permutations of tensor indices and Einstein's sum rule for repeated indices. Using the second approach, LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEiakYnRi9GNUY4RjtGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn represents an abstract non-commutative differentiation operator with respect to the coordinates which acts over expressions that involve a test function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNiUtRiw2KlEiWEYnRi8vJStmb3JlZ3JvdW5kR1EsWzEyOCwxMjgsMF1GJ0YyRjUvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRidGMi9GNlEnbm9ybWFsRidGMkZMRkZGSUYyRkw=. In the end, LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEiakYnRi9GNUY4RjtGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn is given an explicit form in coordinate representation, the differentiation operations are performed and the test function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2KlEiWEYnRi8vJStmb3JlZ3JvdW5kR1EsWzEyOCwxMjgsMF1GJ0YyRjUvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRidGMi9GNlEnbm9ybWFsRidGMkZMRjJGTA== is removed, yielding a result. Presenting both approaches is of interest as it offers two independent methods for performing the same computation, which is helpful to provide confidence in the results, a relevant issue when using computer algebra and in general.In Sec.4, we derive 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 and show that the classical relation between angular momentum and the Runge-Lenz vectors, LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2Ji1JI21pR0YkNilRIkxGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EsWzI1LDczLDExMl1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EsWzI1LDczLDEwNV1GJy1JI21vR0YkNi5RJyZyYXJyO0YnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGV0ZTL0krbXNlbWFudGljc0dGJFEnYXRvbWljRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MFEiLkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUqcmVmZXJlbmNlR1EtWzM1LDEyMCwxNTBdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLVszNSwxMjAsMTQ5XUYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0YvRjI=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, due to the orbital momentum being perpendicular to the plane of motion in which the Runge-Lenz vector lies, still holds in quantum mechanics, where the components of these quantum vector operators do not commute.In Sec.5, we derive 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 using the two alternative approaches described in Sec.3.In Sec.6, we derive the well-known formula for the square of the Runge-Lenz vector, 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.In Sec.7, we use the SO(4) algebra derived in the previous sections to obtain the spectrum of the hydrogen atom. Following the literature, this approach is limited to the bound states for which the energy is negative. Some concluding remarks are presented at the end, and input syntax details are summarized in the Appendix. A Maple worksheet with the contents of this presentation, used to produce this article by exporting to LaTeX, can be downloaded from this Mapleprimes post: The-Hidden-SO4-Symmetry-Of-The-Hydrogen-Atom.<Text-field style="Heading 1" layout="Heading 1">The hidden SO(4) symmetry of the hydrogen atom</Text-field>Let's consider the hydrogen atom and its 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,where 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 is the electron momentum, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2KFEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EsWzI1LDczLDExMl1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EsWzI1LDczLDEwNV1GJy1GLzYoUSJlRidGMkY1RjhGO0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y1LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GOVEnbm9ybWFsRic= its mass, LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEoJmthcHBhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRi4vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn a real positive constant, 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 the distance of the electron from the proton located at the origin, and LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9JK21zZW1hbnRpY3NHRiRRLlBoeXNpY3NUZW5zb3JGJy8lKnJlZmVyZW5jZUdRLVszNSwxMjAsMTUwXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUS1bMzUsMTIwLDE0OV1GJy1JJW1yb3dHRiQ2JS1GLDYpUSJhRidGL0YyRjVGOEY+RkFGMi9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==, with components LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjk2LlEifkYnRjJGPEY+L0ZBRjRGQkZERkZGSEZKRkwvRlBGTi1GLDYmUSJ5RidGL0YyRjVGMkY8 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, is the tensorial representation of 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. We assume that the proton's mass is infinite. The electron and nucleus spin are not taken into account. Classically, from the potential LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2MFEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSy1JJm1mcmFjR0YkNigtSSNtaUdGJDYoUSgma2FwcGE7RicvJSdpdGFsaWNHRjFGL0YyRjVGOC1GUjYoUSJyRicvRlZRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl1vLyUpYmV2ZWxsZWRHRjEtRlI2I1EhRidGL0Yy, one can derive a central force LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkmbW92ZXJHRiQ2JS1JI21pR0YkNihRIkZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKnJlZmVyZW5jZUdRLFsyNSw3MywxMTJdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLFsyNSw3MywxMDVdRictSSNtb0dGJDYwUScmcmFycjtGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj4vJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXRlMtRkI2MFEpJmVxdWFscztGJ0Y1RkVGO0Y+RkdGSS9GTEY3Rk1GT0ZRRlNGVUZYLUZCNjBRKiZ1bWludXMwO0YnRjVGRUY7Rj5GR0ZJRmduRk1GT0ZRRlMvRlZRLDAuMjIyMjIyMmVtRicvRllGXG8tRi82KFEnJiM5NTQ7RicvRjNGN0Y1RkVGO0Y+LUZCNjBRIn5GJ0Y1RkVGO0Y+RkdGSUZnbkZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRmZvLUkmbWZyYWNHRiQ2KC1GIzYpLUZCNi5RMSZJbnZpc2libGVUaW1lcztGJ0Y1RkVGR0ZJRmduRk1GT0ZRRlNGZW9GZ28tRiw2JS1GLzYoUSJyRidGMkY1RjhGO0Y+LUZCNjBRKCZ3ZWRnZTtGJ0Y1RkVGO0Y+RkdGSUZnbkZNRk9GUUZTL0ZWUSwwLjE2NjY2NjdlbUYnL0ZZRmlwRlMvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRidGNS8lKXJlYWRvbmx5R0Y0LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RidGRS1JJW1zdXBHRiQ2JUZicC1JI21uR0YkNidRIjJGJ0Y1RkVGO0Y+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYnIvJSliZXZlbGxlZEdGN0ZbcUY1Rl5xRmBxRkU= that drives the electron's motion. Introducing the angular 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,one can further define the Runge-Lenz vector 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 is well known that 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtb3ZlckdGJDYlLUYsNihRIlpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKnJlZmVyZW5jZUdRLFsyNSw3MywxMTJdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLFsyNSw3MywxMDVdRictSSNtb0dGJDYwUScmcmFycjtGJ0Y4L0Y8USdub3JtYWxGJ0Y+RkEvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRlZGOEZI is a constant of the motion. Switching to Quantum Mechanics, this condition 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, for hermiticity purpose, the expression of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbW92ZXJHRiQ2JS1JI21pR0YkNilRIlpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EsWzI1LDczLDExMl1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EsWzI1LDczLDEwNV1GJy1JI21vR0YkNjBRJyZyYXJyO0YnRjgvRjxRJ25vcm1hbEYnRj5GQS8lJmZlbmNlR0Y6LyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlpGVi1GLzYjUSFGJ0Y4Rkg= must be 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 what follows, departing from the Hamiltonian H, the basic commutation rules between position LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtb3ZlckdGJDYlLUYsNilRInJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKnJlZmVyZW5jZUdRLFsyNSw3MywxMTJdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLFsyNSw3MywxMDVdRictSSNtb0dGJDYuUScmcmFycjtGJ0Y7L0Y/USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0ZPLyUobGFyZ2VvcEdGTy8lLm1vdmFibGVsaW1pdHNHRk8vJSdhY2NlbnRHRk8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZobkZaRjtGSw==, momentum 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 and angular momentum 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 in tensor notation, we derive the following commutation rules between the quantum Hamiltonian, angular momentum and Runge-Lenz vector 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
Since H commutes with both 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 and 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, 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these commutation rules can be rewritten as
This set constitutes the Lie algebra of the SO(4) group.<Text-field style="Heading 1" layout="Heading 1">Setting the problem, commutation rules and useful identities</Text-field>Formulating the problem requires loading the Physics package and its Library and Vectors subpackages, that contain additional manipulation commands; we set the imaginary unit to be represented by a lowercase Latin i letter instead of the default uppercase I.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The context for this problem is Cartesian coordinates LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JKG1mZW5jZWRHRiQ2JS1GIzYpLUYsNiZRInhGJ0YvRjJGNS1GOTYuUSIsRidGMkY8Rj4vRkFGMUZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RlktRiw2JlEiekYnRi9GMkY1RjJGPEYyRjxGMkY8 and a 3D Euclidean space where all of 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 are real objects. We chose lowercase letters to represent tensor indices, the use of automatic simplification (i.e., automatically rewrite expressions in more compact ways by collecting variables and taking common factors) 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Next, we set the quantum Hermitian operators (not Z, we derive that property for it further below) and related commutators:the dimensionless potential LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EsWzI1LDczLDExMl1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EsWzI1LDczLDEwNV1GJy1JI21vR0YkNjBRIn5GJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWC1GQjYwUSI9RidGNUZFRjtGPkZHRkpGTEZORlBGUkZUL0ZXUSwwLjI3Nzc3NzhlbUYnL0ZaRmluRkEtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2J1EiMUYnRjVGRUY7Rj4tRiM2Ji1GLDYpUSJyRidGL0YyRjVGOEY7Rj5GL0Y1RjgvJS5saW5ldGhpY2tuZXNzR0Zhby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcC8lKWJldmVsbGVkR0ZJRjVGRQ== is assumed to commute with position, not with momentum - the commutation rule with LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= is derived in Sec.3.2;the commutator rules between position LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibkYnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= on the one hand, and linear LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= and angular momentum LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= on the other hand, are the departure point, entered using the inert form of the Commutator command. Tensors are indexed using the standard Maple notation for indexation, [].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 the tensor quantum operators representing the linear momentum, angular momentum and the Runge-Lenz vectorsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSdEZWZpbmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2LS1GLDYlUSJwRidGNEY3LUY7NiYtRiM2JC1GLDYlUSJrRidGNEY3L0Y4USdub3JtYWxGJ0ZJLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUkjbW9HRiQ2LVEiLEYnRkkvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGVy8lKnN5bW1ldHJpY0dGVy8lKGxhcmdlb3BHRlcvJS5tb3ZhYmxlbGltaXRzR0ZXLyUnYWNjZW50R0ZXLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiTEYnRjRGN0ZCRlEtRiw2JVEiWkYnRjRGN0ZCRlEtRiw2JVEmcXVpZXRGJ0Y0RjdGSUZJRklGKy8lK2V4ZWN1dGFibGVHRldGSQ==For readability, avoid redundant display of functionalityLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUS9Db21wYWN0RGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUY7NiQtRiM2Ji1GLDYlUSJWRidGNEY3LUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZOLyUqc3ltbWV0cmljR0ZOLyUobGFyZ2VvcEdGTi8lLm1vdmFibGVsaW1pdHNHRk4vJSdhY2NlbnRHRk4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJHRidGNEY3RkpGSi1GOzYkLUYjNiUtRiw2JlEiWEYnRjRGNy9JK21zZW1hbnRpY3NHRiRRLlBoeXNpY3NUZW5zb3JGJy8lK2V4ZWN1dGFibGVHRk5GSkZKRitGSkZKRkpGK0Zob0ZKThe Hamiltonian for the hydrogen atom is entered 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.<Text-field style="Heading 2" layout="Heading 2"><Font size="14">Definition of V(X) and related identities</Font></Text-field>We use the dimensionless potential 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 gradient of 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 is 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 we note that all these commands (including product and power), distribute over equations. So 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Equivalently, from one can 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 will often be used afterwards.<Text-field style="Heading 2" layout="Heading 2">The commutation rules between linear and angular momentum and of the potential V(X)</Text-field>By 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 commutator on the right-hand side cannot be computed by the CAS until more information is provided. To derive the value of 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we set LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibkYnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= as a differentialoperator and introduce an arbitrary test function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EtWzM1LDEyMCwxNTBdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLVszNSwxMjAsMTQ5XUYnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2KlEiWEYnRi8vJStmb3JlZ3JvdW5kR1EsWzEyOCwxMjgsMF1GJ0YyRjUvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRidGOEY7RjIvRjZRJ25vcm1hbEYnRjJGTEYyRkw=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Apply now to 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 the differential operator LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibkYnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= found in the commutator of the right-hand side of 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The result of 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 is not known to the system at this point. Define then an explicit representation for LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictSSVtcm93R0YkNiUtRiw2JlEibkYnRi9GNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= as the differential operator in configuration space 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where in the above LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEjb3BGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUYsNiZRKXByb2NuYW1lRidGL0YyRjVGMi9GNlEnbm9ybWFsRidGMkZALyUqcmVmZXJlbmNlR1EtWzM1LDEyMCwxNTBdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLVszNSwxMjAsMTQ5XUYnRjJGQA== represents the indices with which the differential operator LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictSSVtcm93R0YkNiUtRiw2JlEibkYnRi9GNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= is called.With this definition, the right-hand side of automatically evaluates toLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FcYG8vLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkrQ29tbXV0YXRvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkiTEc2IjYjSSJxRzYiLUkiVkc2IjYjSSJYRzYiLUkiR0c2IjYjSSJYRzYiKiYmSStMZXZpQ2l2aXRhRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiVJIm1HNiJJIm5HNiJJInFHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJIm1HNiI2I0kiWEc2IiwmLSZJInBHNiI2I0kibkc2IjYjLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiLUkiR0c2IjYjSSJYRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiLSZJInBHNiI2I0kibkc2IjYjLUkiR0c2IjYjSSJYRzYiISIiIiIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMDM1KUYnLyUldmlld0dRJmxhYmVsRidGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==So that using LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LlEoJmVxdWl2O0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRS1GIzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2KVErJlBhcnRpYWxEO0YnLyUnaXRhbGljR1EldHJ1ZUYnRi8vRjNRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEqUGh5c2ljc2RfRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRk42KFEibkYnRlFGL0ZURllGZm4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLDYuUTAmQXBwbHlGdW5jdGlvbjtGJ0YvRjJGNUY3RjlGO0Y9Rj9GQS9GRFEmMC4wZW1GJy9GR0Zjby1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUZONilRIlZGJ0ZRLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRidGL0ZURllGZm5GL0YyRi9GMkZZRmZuRi9GMi1GLDYwUSkmZXF1YWxzO0YnRi9GMkZZRmZuRjVGN0Y5RjtGPUY/RkFGQ0ZGLUYjNictRiw2MFEoJm1pbnVzO0YnRi9GMkZZRmZuRjVGN0Y5RjtGPUY/RkEvRkRRLDAuMjIyMjIyMmVtRicvRkdGaXAtRiM2Jy1JJW1zdXBHRiQ2JkZqby1JI21uR0YkNidRIjNGJ0YvRjJGWUZmbi8lMXN1cGVyc2NyaXB0c2hpZnRHRl5vL0ZXUSJeRictRiw2LlExJkludmlzaWJsZVRpbWVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRmJvRmRvLUZLNiUtRk42KlEiWEYnRlFGXXBGL0ZUL0ZXUS5QaHlzaWNzVGVuc29yRidGWUZmbkZpbkZcb0YvRjItRk42I1EhRidGL0YyRmJyRi9GMg== and multiplying by 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, 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from where we get the first commutation rule: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Likewise, from the 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 form of 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by applying this equation to the test function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUkobWZlbmNlZEdGJDYnLUYjNiUtRiw2KlEiWEYnRi9GMkY1RjgvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRidGO0Y+RjUvRjlRJ25vcm1hbEYnRjVGTEY7Rj5GNUZM we 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In the same way, for 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we 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now these new commutation rules to the setup of the problem, they will be taken into account in subsequent uses of 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 differentialoperators to work using two different approaches, with and without them.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Commutation rules between the Hamiltonian and each of the angular momentum and Runge-Lenz tensorsDeparting from the Hamiltonian 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 and the definition of angular momentum 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, by taking their commutator we getLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUStDb21tdXRhdG9yRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNihGKy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWZ4L0kiSEc2IiwmKigjIiIiIiIjIiIiSSVtX19lRzYiISIiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkicEc2IjYjSSJsRzYiIiIjIiIiIiIiKiZJJmthcHBhRzYiIiIiLUkiVkc2IjYjSSJYRzYiIiIiISIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMTU4KUYnLyUldmlld0dRJmxhYmVsRictSSNtb0dGJDYtUSIsRicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRlQvJSpzeW1tZXRyaWNHRlQvJShsYXJnZW9wR0ZULyUubW92YWJsZWxpbWl0c0dGVC8lJ2FjY2VudEdGVC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZANiUtRkM2I1FkaGwvJkkiTEc2IjYjSSJxRzYiKiYmSStMZXZpQ2l2aXRhRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiVJIm1HNiJJIm5HNiJJInFHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJIm1HNiI2I0kiWEc2IiZJInBHNiI2I0kibkc2IiIiIkYnL0ZHUT1tYXBsZXNvZnQuY29tOmxhYmVsKEw5MzIyMDgpRidGSUYrRlBGUEZQRisvJStleGVjdXRhYmxlR0ZURlA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpU2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUV5bcC8tSStDb21tdXRhdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiRJIkhHNiImSSJMRzYiNiNJInFHNiIsJCosLCReIyIiIiIiIiIiIiZJK0xldmlDaXZpdGFHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JUkibUc2Ikkibkc2IkkicUc2IiIiIkknJmhiYXI7RzYiIiIiLCYqKC1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JS0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kibUc2IjYjSSJYRzYiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIkLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJuRzYiNiNJIlhHNiIiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiISIiKiYtSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQmSSJwRzYiNiNJImxHNiImSSJwRzYiNiNJIm5HNiIiIiImSSNnX0c2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkSSJsRzYiSSJtRzYiIiIiIiIiIiIiSSVtX19lRzYiISIiISIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMDI1KUYnLyUldmlld0dRJmxhYmVsRidGOi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZNRkpGTQ==<Text-field style="Heading 2" layout="Heading 2">The commutator between the Hamiltonian and Runge-Lenz tensor: algebraic approach</Text-field>Start from the definition of the quantum Runge-Lenz 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 tensor is HermitianLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FkX24vJkkiWkc2IjYjSSJrRzYiLCYqKiMiIiIiIiMiIiJJJW1fX2VHNiIhIiImSStMZXZpQ2l2aXRhRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiVJImFHNiJJImJHNiJJImtHNiIiIiIsJi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCZJIkxHNiI2I0kiYUc2IiZJInBHNiI2I0kiYkc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCZJInBHNiI2I0kiYUc2IiZJIkxHNiI2I0kiYkc2IiEiIiIiIiIiIiomSSZrYXBwYUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JIlZHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiIiIiIiIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMTU5KUYnLyUldmlld0dRJmxhYmVsRictSSNtb0dGJDYtUSgmbWludXM7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlQtRiw2JVEnRGFnZ2VyRicvJSdpdGFsaWNHUSV0cnVlRicvRkFRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNidGK0YvRisvJStleGVjdXRhYmxlR0ZFRkBGQEYrRl5vRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpU2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWdjcS8sJiZJIlpHNiI2I0kia0c2IiIiIi1JJ0RhZ2dlckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjJkkiWkc2IjYjSSJrRzYiISIiLCQqKCMiIiIiIiMiIiIsKCoqIiIjIiIiSSZrYXBwYUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JIlZHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiIiIiSSVtX19lRzYiIiIiIiIiKioiIiMiIiJJJmthcHBhRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJrRzYiNiNJIlhHNiItSSJWRzYiNiNJIlhHNiIiIiJJJW1fX2VHNiIiIiIhIiIqJiZJK0xldmlDaXZpdGFHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JUkiYUc2IkkiYkc2Ikkia0c2IiIiIiwqLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkiTEc2IjYjSSJhRzYiJkkicEc2IjYjSSJiRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkiTEc2IjYjSSJiRzYiJkkicEc2IjYjSSJhRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkicEc2IjYjSSJhRzYiJkkiTEc2IjYjSSJiRzYiISIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkicEc2IjYjSSJiRzYiJkkiTEc2IjYjSSJhRzYiISIiIiIiIiIiIiIiSSVtX19lRzYiISIiIiIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMDMzKUYnLyUldmlld0dRJmxhYmVsRidGOi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZNRkpGTQ==Since the system knows about the commutation rule between linear and angular momentum,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 expression for LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYsNihRImtGJ0YvRjVGOEY+RkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== can be 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 the angular momentum removed from the the right-hand side using 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, so that LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYsNihRImtGJ0YvRjVGOEY+RkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== gets expressed entirely in terms of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KlEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYvNihRImtGJ0YyRjhGO0ZBRkQvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y4L0Y8USdub3JtYWxGJw==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnRjUvRjlRJ25vcm1hbEYn and 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 the commutator between 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, and this expression for LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYsNihRImtGJ0YvRjVGOEY+RkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== we have the starting point towards showing that 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In order to use the 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sort the products using the ordering shown in the left-hand 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this is the result we wanted to prove.<Text-field style="Heading 2" layout="Heading 2">The commutator between the Hamiltonian and Runge-Lenz tensor: alternative derivation using differential operators</Text-field>As done in the previous section when deriving the commutators between linear and angular momentum, on the one hand, and the central potential LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnRjUvRjlRJ25vcm1hbEYn on the other hand, the idea here is again to use differential operators taking advantage of the ability to compute with them as operands of a product, that get applied only when it appears convenient for 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So take the starting point 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 to show that the right-hand side is equal to 0, multiply by a generic function 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 followed by transforming the products involving LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYjNigtRi82JlEibkYnRjJGOEY7RjJGOEY7Rj5GQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjgvRjxRJ25vcm1hbEYn into the application of this differential operator 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addition, consider the application of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRi82JlEibEYnRjJGOEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRKlswLDAsMjU1XUYnRjgvJSlyZWFkb25seUdGNC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnL0Y8USdub3JtYWxGJw== to the test function 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 this identity together with the derived identity 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, followed by multiplying by 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 to remove the test function from the equation, we 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Applying 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to the setup these derived commutation rules between the Hamiltonian, angular momentum and Runge-Lenz 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 differentialoperators in order to proceed to the next section working without 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<Text-field style="Heading 1" layout="Heading 1">Commutation rules between the angular momentum and the Runge-Lenz tensors</Text-field>Departing from the definition of these tensors, introduced in the previous 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 left-hand side of the identity to be proved is the left-hand side of the commutator of these two 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By eye, the right-hand side of is similar to the right-hand side of the definition of LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= in , so introduce this definition directly into the right-hand side of . For that purpose, isolate 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Simplifying, we get the desired result, and we substitute the active by the inert form of Commutator for later use of this formula without having the Commutator automatically executed.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Set now this algebra rule to be available to the system when convenientLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmU2V0dXBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYjUSFGJ0Y6LUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRXVtsLy1JLCVDb21tdXRhdG9yRzYiNiQmSSJMRzYiNiNJInFHNiImSSJaRzYiNiNJImtHNiIsJCoqLCReIyIiIiIiIiIiIkknJmhiYXI7RzYiIiIiJkkrTGV2aUNpdml0YUc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlSSJhRzYiSSJrRzYiSSJxRzYiIiIiJkkiWkc2IjYjSSJhRzYiIiIiISIiRicvJSthY3Rpb250eXBlR1E9bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTMyMDk3KUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRidGSkY6LyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGSg==<Text-field style="Heading 2" layout="Heading 2">The scalar product between the quantized angular momentum and the Runge-Lenz tensors</Text-field>Classically, the orbital momentum is perpendicular to the plane of motion, while the Runge-Lenz vector lies in that plane, so that 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. In quantum mechanics, from 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 but 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 = 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 still holds. To verify that, take the definition of the quantum Runge-Lenz vector and multiply it by 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MFEoJmVxdWl2O0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUqcmVmZXJlbmNlR1EqWzM2LDUsNTRdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRKlszNiw1LDUzXUYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YvRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2KlEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRi82KFEicUYnRjJGOEY7RkFGRC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2MFEpJmVxdWFscztGJ0Y4L0Y8USdub3JtYWxGJ0ZBRkQvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zdby1GIzYqLUYsNiUtRi82KVEqJmVwc2lsb247RicvRjNGOkY4RlEvRj9RMlBoeXNpY3NMZXZpQ2l2aXRhRidGQUZELUYjNiwtRi82KFEibUYnRjJGOEY7RkFGRC1GTjYwUSgmY29tbWE7RidGOEZRRkFGREZTL0ZWRjRGV0ZZRmVuRmduRmluL0Zcb1EmMC4wZW1GJy9GX29RLDAuMzMzMzMzM2VtRictRi82KFEibkYnRjJGOEY7RkFGREZfcEZHL0Y2USpbMCwwLDI1NV1GJ0Y4LyUpcmVhZG9ubHlHRjQvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0ZRRkotRk42LlExJkludmlzaWJsZVRpbWVzO0YnRjhGUUZTRlVGV0ZZRmVuRmduRmluRmNwL0Zfb0ZkcC1GIzYqLUYsNiUtRi82KlEiWEYnRjJGNUY4RjtGPkZBRkRGXHBGSkZhcS1GLDYlLUYvNipRInBGJ0YyRjVGOEY7Rj5GQUZERmdwRkpGanBGOEZccUZecUZRRmpwRjhGXHFGXnFGUUZqcEY4RlxxRl5xRlE=,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due to 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reversing the order in the product,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<Text-field style="Heading 1" layout="Heading 1">Commutation rules between the components of the Runge-Lenz tensor</Text-field>Here again the starting point is , the definition of the quantum Runge-Lenz 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The commutator LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYnLUklbXJvd0dGJDYoLUYvNiotRiM2JS1JI21pR0YkNihRIlpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEuUGh5c2ljc1RlbnNvckYnLUY2NiZRImtGJ0Y5Rj9GQi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEoJmNvbW1hO0YnRj8vRkNRJ25vcm1hbEYnLyUmZmVuY2VHRkEvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiM2JUY1LUY2NiZRInFGJ0Y5Rj9GQkZLL0Y9USpbMCwwLDI1NV1GJ0Y/LyUpcmVhZG9ubHlHRjsvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0ZSRmdvRj9GaW9GW3BGUkY/RlIvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnLUZPNi5RKCZtaW51cztGJ0Y/RlJGVC9GV0ZBRlhGWkZmbkZobkZqbi9GXW9RLDAuMjIyMjIyMmVtRicvRmBvRmlwRksvRkZRMlBoeXNpY3NDb21tdXRhdG9yRic=is computed 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order to use LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2MVEoJmVxdWl2O0YnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZOLUklbXN1cEdGJDYmLUkjbWlHRiQ2KVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnRi9GMi9GNlEnaXRhbGljRidGOEY7LUkjbW5HRiQ2JVEiM0YnRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSJeRictRiw2LlExJkludmlzaWJsZVRpbWVzO0YnRjJGNUY+RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRmVvLUZSNiYtSSVtc3ViR0YkNiUtRlU2KFEiWEYnRlhGL0YyRmVuL0Zfb1EuUGh5c2ljc1RlbnNvckYnLUZVNiZRImxGJ0ZYRjJGZW4vJS9zdWJzY3JpcHRzaGlmdEdGXW8tRmhuNiVRIjJGJ0YyRjVGW29GXm8tRiw2LlEpJmVxdWFscztGJ0YyRjVGPkZARkJGREZGRkhGSkZMRk8tRlU2J0ZXRlhGL0YyRmVuRjJGNQ==, sort the products in using the ordering 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the quadratic term in the momentum, from the expression for the Hamiltonian 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order to use this equation to substitute LUkobXN1YnN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibEYnRi9GNUY4LUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZJ into the expression for 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 and not receive noncommutative products with 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSJ+RidGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRRjVGPw==and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ji1GLzYmUSJxRidGMkY4RjtGMkY4RjsvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y4L0Y8USdub3JtYWxGJw==) , sort first the products in positioning all square of momentums 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Finally, from the definition of the angular momentum 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, multiplying by 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 we can construct an expression for 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 in terms of LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictSSVtcm93R0YkNiYtRiw2JlEicUYnRi9GNUY4Ri9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=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is the identity we wanted to prove.<Text-field style="Heading 2" layout="Heading 2">Alternative derivation using differential operators</Text-field>Set again the differentialoperator representation for the momentum operator LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=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and apply the expression for LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYnLUklbXJvd0dGJDYoLUYvNiotRiM2JS1JI21pR0YkNihRIlpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEuUGh5c2ljc1RlbnNvckYnLUY2NiZRImtGJ0Y5Rj9GQi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEoJmNvbW1hO0YnRj8vRkNRJ25vcm1hbEYnLyUmZmVuY2VHRkEvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiM2JUY1LUY2NiZRInFGJ0Y5Rj9GQkZLL0Y9USpbMCwwLDI1NV1GJ0Y/LyUpcmVhZG9ubHlHRjsvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0ZSRmdvRj9GaW9GW3BGUkY/RlIvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnLUZPNi5RKCZtaW51cztGJ0Y/RlJGVC9GV0ZBRlhGWkZmbkZobkZqbi9GXW9RLDAuMjIyMjIyMmVtRicvRmBvRmlwRksvRkZRMlBoeXNpY3NDb21tdXRhdG9yRic=to the test function 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eXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiIiIiIiIiIqKiMiIiIiIiQiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYpLUkiVkc2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kicUc2IjYkLUkiVkc2IjYjSSJYRzYiNyNJIlhHNiItSSJHRzYiNiNJIlhHNiItSSJWRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiIiIiISIiKiojIiIjIiIkIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2KS1JIlZHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2JC1JIlZHNiI2I0kiWEc2IjcjSSJYRzYiLUkiR0c2IjYjSSJYRzYiLUkiVkc2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2IiIiIiEiIioqIyIiIyIiJCIiIkkma2FwcGFHNiIiIiJJJW1fX2VHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiktSSJWRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2I0kiWEc2Ii0mSSNkX0c2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiQtSSJWRzYiNiNJIlhHNiI3I0kiWEc2Ii1JIkdHNiI2I0kiWEc2Ii1JIlZHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiIiIiIiIiIqKiMiIiIiIiQiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIjLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYkLUkiVkc2IjYjSSJYRzYiNyNJIlhHNiItSSJHRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiIiIiIiIiKiojIiIiIiIkIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2KC1JIl5HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JIlZHNiI2I0kiWEc2IiIiIy0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2JC1JIlZHNiI2I0kiWEc2IjcjSSJYRzYiLUkiR0c2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJrRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2IiIiIiEiIioqIyIiIyIiJCIiIkkma2FwcGFHNiIiIiJJJW1fX2VHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNigtSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSJWRzYiNiNJIlhHNiIiIiMtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2I0kiWEc2Ii0mSSNkX0c2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiQtSSJWRzYiNiNJIlhHNiI3I0kiWEc2Ii1JIkdHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kicUc2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiIiIiIhIiIqKiMiIiMiIiQiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIjLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYkLUkiVkc2IjYjSSJYRzYiNyNJIlhHNiItSSJHRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiIiIiIiIiKiojIiIiIiIkIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2KC0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2JC1JIlZHNiI2I0kiWEc2IjcjSSJYRzYiLUkiR0c2IjYjSSJYRzYiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIjLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2IiIiIiIiIioqIyIiIiIiJCIiIkkma2FwcGFHNiIiIiJJJW1fX2VHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNigtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2Ii0mSSNkX0c2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiQtSSJWRzYiNiNJIlhHNiI3I0kiWEc2Ii1JIkdHNiI2I0kiWEc2Ii1JIl5HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JIlZHNiI2I0kiWEc2IiIiIy0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJkRzYiNiNJIlhHNiIiIiIhIiIqKiMiIiMiIiQiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJrRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYkLUkiVkc2IjYjSSJYRzYiNyNJIlhHNiItSSJHRzYiNiNJIlhHNiItSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSJWRzYiNiNJIlhHNiIiIiMtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiIiIiISIiKiojIiIjIiIkIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2KC0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kicUc2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2JC1JIlZHNiI2I0kiWEc2IjcjSSJYRzYiLUkiR0c2IjYjSSJYRzYiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIjLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJrRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2IiIiIiIiIioqIyIiIiIiJCIiIkkma2FwcGFHNiIiIiJJJW1fX2VHNiIiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiYtSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSJWRzYiNiNJIlhHNiIiIiQtSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImRHNiI2I0kiWEc2IiIiIy0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2JC1JIkdHNiI2I0kiWEc2IjcjSSJYRzYiIiIiISIiKiojIiIiIiIkIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Ji1JIl5HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JIlZHNiI2I0kiWEc2IiIiJC1JIl5HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiZEc2IjYjSSJYRzYiIiIjLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYkLUkiR0c2IjYjSSJYRzYiNyNJIlhHNiIiIiIiIiIqKiMiIiIiIiQiIiJJJmthcHBhRzYiIiIiSSVtX19lRzYiIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmLUkiR0c2IjYjSSJYRzYiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiVkc2IjYjSSJYRzYiIiIkLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJrRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2I0kiWEc2IiIiIiEiIiooIyIiIiIiJCIiIilJJyZoYmFyO0c2IiIiIyIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInFHNiI2JC1JLWRBbGVtYmVydGlhbkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiR0c2IjYjSSJYRzYiNyNJIlhHNiI3I0kiWEc2IiIiIiIiIiooIyIiIiIiJCIiIilJJyZoYmFyO0c2IiIiIyIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kicUc2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2JC1JLWRBbGVtYmVydGlhbkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiR0c2IjYjSSJYRzYiNyNJIlhHNiI3I0kiWEc2IiIiIiEiIiooSSVtX19lRzYiIiIiLCgtSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiUtSSJWRzYiNiNJIlhHNiItJkkwU3BhY2VUaW1lVmVjdG9yRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2I0kiWEc2Ii0mSSNkX0c2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiQtSSJHRzYiNiNJIlhHNiI3I0kiWEc2IiIiIi1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JS1JIlZHNiI2I0kiWEc2Ii0mSTBTcGFjZVRpbWVWZWN0b3JHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kicUc2IjYjSSJYRzYiLSZJI2RfRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJImtHNiI2JC1JIkdHNiI2I0kiWEc2IjcjSSJYRzYiISIiKiYjIiIiIiIkIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlLSZJMFNwYWNlVGltZVZlY3Rvckc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJxRzYiNiNJIlhHNiItJkkjZF9HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kia0c2IjYkLUkiVkc2IjYjSSJYRzYiNyNJIlhHNiItSSJHRzYiNiNJIlhHNiIiIiIhIiIiIiJJJmthcHBhRzYiIiIiIiIiRicvRmhvUT1tYXBsZXNvZnQuY29tOmxhYmVsKEw5MzIyMzUpRidGam9GXW9GYHBGL0YvRmBwRi9GL0ZgcEYvEvaluating the term 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 this result into the expression forLUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYnLUklbXJvd0dGJDYoLUYvNiotRiM2JS1JI21pR0YkNihRIlpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSxbMTI4LDEyOCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEuUGh5c2ljc1RlbnNvckYnLUY2NiZRImtGJ0Y5Rj9GQi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEoJmNvbW1hO0YnRj8vRkNRJ25vcm1hbEYnLyUmZmVuY2VHRkEvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiM2JUY1LUY2NiZRInFGJ0Y5Rj9GQkZLL0Y9USpbMCwwLDI1NV1GJ0Y/LyUpcmVhZG9ubHlHRjsvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0ZSRmdvRj9GaW9GW3BGUkY/RlIvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnLUZPNi5RKCZtaW51cztGJ0Y/RlJGVC9GV0ZBRlhGWkZmbkZobkZqbi9GXW9RLDAuMjIyMjIyMmVtRicvRmBvRmlwRksvRkZRMlBoeXNpY3NDb21tdXRhdG9yRic=and removing the test function multiplying by 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 expression can be 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the identity 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for the 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using 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which is the expected result. Set now differential operators to none.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<Text-field style="Heading 1" layout="Heading 1">The square of the norm of the Runge-Lenz vector</Text-field>Taking the square of the definition of LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRiw2KFEia0YnRi9GNUY4Rj5GQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn and 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 the algebraic properties of the 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the expression for LUkobXN1YnN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEia0YnRi9GNUY4LUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZJ 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 term having 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 can be simplified using the expression of the momentum 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Reordering to have the two terms with four operators sorted as 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Considering now the resulting single term 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, it can be shown it is equal to zero using the definition 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 this result into account, we have, for LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2KlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRicvJSpyZWZlcmVuY2VHUS1bMzUsMTIwLDE1MF1GJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1EtWzM1LDEyMCwxNDldRictRi82KFEia0YnRjJGOEY7RkFGRC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW5HRiQ2J1EiMkYnRjgvRjxRJ25vcm1hbEYnRkFGRC8lMXN1cGVyc2NyaXB0c2hpZnRHRkwvRj9RIl5GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSVzdWJzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNilGKy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWl2Ly1JIipHNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JiZJInBHNiI2I0kiYUc2IiZJInBHNiI2I0kiYkc2IiZJIkxHNiI2I0kiYUc2IiZJIkxHNiI2I0kiYkc2IiIiIUYnLyUrYWN0aW9udHlwZUdRPW1hcGxlc29mdC5jb206bGFiZWwoTDkzMjI1MSlGJy8lJXZpZXdHUSZsYWJlbEYnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZULyUqc3ltbWV0cmljR0ZULyUobGFyZ2VvcEdGVC8lLm1vdmFibGVsaW1pdHNHRlQvJSdhY2NlbnRHRlQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GQDYlLUZDNiNRamNwLywkKigiIiMiIiIpSSVtX19lRzYiIiIjIiIiLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkiWkc2IjYjSSJrRzYiIiIjIiIiIiIiLC4qLCIiJSIiIkkma2FwcGFHNiIiIiIpSScmaGJhcjtHNiIiIiMiIiItSSJWRzYiNiNJIlhHNiIiIiJJJW1fX2VHNiIiIiIhIiIqKCIiIyIiIilJJmthcHBhRzYiIiIjIiIiKUklbV9fZUc2IiIiIyIiIiIiIioqIiIlIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiXkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJkkiTEc2IjYjSSJhRzYiIiIjLUkiVkc2IjYjSSJYRzYiIiIiSSZrYXBwYUc2IiIiIkklbV9fZUc2IiIiIiEiIiomIiIjIiIiLUkiKkc2JiUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIvSTFoaWRlbW9kdWxlcHJlZml4RzYiSSV0cnVlRyUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmJkkicEc2IjYjSSJhRzYiJkkicEc2IjYjSSJiRzYiJkkiTEc2IjYjSSJhRzYiJkkiTEc2IjYjSSJiRzYiIiIiISIiKiYiIiMiIiItSSIqRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQmSSJwRzYiNiNJImFHNiIiIiMtSSJeRzYmJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkoUGh5c2ljc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ii9JMWhpZGVtb2R1bGVwcmVmaXhHNiJJJXRydWVHJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQmSSJMRzYiNiNJImJHNiIiIiMiIiIiIiIqKCIiIyIiIilJJyZoYmFyO0c2IiIiIyIiIi1JIl5HNiYlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSShQaHlzaWNzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiL0kxaGlkZW1vZHVsZXByZWZpeEc2IkkldHJ1ZUclKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCZJInBHNiI2I0kiYUc2IiIiIyIiIiIiIkYnL0ZHUT1tYXBsZXNvZnQuY29tOmxhYmVsKEw5MzIxODApRidGSUYrLyUrZXhlY3V0YWJsZUdGVEZQRlBGaG9GUEYrRmhvRlA=Substituting now 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Equalizing the repeated indices, the right-hand side can be 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which is the result we wanted to demonstrate.<Text-field style="Heading 1" layout="Heading 1">The atomic hydrogen spectrum</Text-field>We now have all the algebra to reconstruct the hydrogen spectrum. Following the literature, this approach is limited to the bound states for which the energy is negative. Assuming an eigenstate of H with negative eigenvalue E, we replace the Hamiltonian H by E, and look for the possible values of E. Another way to state the same thing is that the analysis is restricted to the subspace of energy E. The operator 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, is introduced as mentioned in Sec.1. The operators J and K, to be used soon after, are added to the formulation of the 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The domain for LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUklbXJvd0dGJDYmLUYsNiZRImVGJ0YvRjJGNUYyLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0Yn and LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn is set 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Recalling the commutation rules 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 and above with E replacing 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Isolating the commutator, the expression for 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appears rewritten in terms of the LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEia0YnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= 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Likewise, inserting 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 into the expression 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, we get it rewritten in terms of 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Add these two newly derived commutators to the 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These commutators , , together with the departing 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constitute a closed form, the algebra of the SO(4) group, that is, the rotation group in dimension 4.We now define the two operators J and K as 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 M and L both commute with H (since M is proportional to Z up-to a commutative factor), it is straightforward to see that J and K also commute with H. They are therefore constants of the motion. Additionally, because at this point (see ) the system already knows about the commutators 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 and 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, the commutator between the components of LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibUYnRi9GNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= results 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In a similar 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 J and K have the symmetry of a rotation operator in two independent 3 dimension spaces. H then has the symmetry of the group LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEjU09GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0YxLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUkjbW5HRiQ2JVEiM0YnRjJGNEYyRjRGMkY0LUkjbW9HRiQ2LlEpJm90aW1lcztGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZURitGN0YyRjQ=. Furthermore, one knows that the possible eigenvalues for the rotation operators J and K are 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 and 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, with 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. Computing now LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2KVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYjNiYtSSNtbkdGJDYnUSIyRidGOC9GPFEnbm9ybWFsRicvRj9RLVszNSwxMjAsMTUwXUYnL0ZCUS1bMzUsMTIwLDE0OV1GJ0YyRjhGOy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOEZKLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnRXhwYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSVtc3VwR0YkNiUtSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FfcC8mSSJKRzYiNiNJIm1HNiIsJiomIyIiIiIiIyIiIiZJIkxHNiI2I0kibUc2IiIiIiIiIiomIyIiIiIiIyIiIiZJIk1HNiI2I0kibUc2IiIiIiIiIkYnLyUrYWN0aW9udHlwZUdRPW1hcGxlc29mdC5jb206bGFiZWwoTDkzMjAwMClGJy8lJXZpZXdHUSZsYWJlbEYnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnRi9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZQRlBGVUZQRecalling 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, and considering that M is proportional to Z, we have that 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, for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2KVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSpyZWZlcmVuY2VHUSxbMjUsNzMsMTEyXUYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSxbMjUsNzMsMTA1XUYnLUYjNiUtSSNtbkdGJDYnUSIyRidGOC9GPFEnbm9ybWFsRicvRj9RLVszNSwxMjAsMTUwXUYnL0ZCUS1bMzUsMTIwLDE0OV1GJ0Y4RkovJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjhGSg==, from 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 that 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That is, 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 which means they share the same eigenvalues, say 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 for a given eigenstate of H with the considered eigenvalue E. Next, inserting 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 into 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 we get an expression for 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 this result into LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MFEoJmVxdWl2O0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUqcmVmZXJlbmNlR1EtWzM1LDEyMCwxNTBdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLVszNSwxMjAsMTQ5XUYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YvRjI=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 and simplifying we 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Taking the average value of LUkobXN1YnN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibUYnRi9GNUY4LUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZJ over an eigenvector, LUkobXN1YnN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMTI4LDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvSSttc2VtYW50aWNzR0YkUS5QaHlzaWNzVGVuc29yRictRiw2JlEibUYnRi9GNUY4LUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZJ can be replaced by its eigenvalue 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from where the possible values of the energy 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Assuming 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, a positive integer and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1EtWzM1LDEyMCwxNTBdRicvJTJkaXNwbGF5X3JlZmVyZW5jZUdRLVszNSwxMjAsMTQ5XUYnLUkjbW9HRiQ2MFEqJkVsZW1lbnQ7RidGMi9GNlEnbm9ybWFsRidGOEY7LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1JKG1mZW5jZWRHRiQ2KS1GIzYyLUkjbW5HRiQ2J1EiMEYnRjJGQkY4RjstRj82MFEiLEYnRjJGQkY4RjtGRC9GR0YxRkhGSkZMRk5GUC9GU1EmMC4wZW1GJy9GVlEsMC4zMzMzMzMzZW1GJy1JJm1mcmFjR0YkNigtRmduNidRIjFGJ0YyRkJGOEY7LUYjNiUtRmduNidRIjJGJ0YyRkJGOEY7RjJGQi8lLmxpbmV0aGlja25lc3NHRmdvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmFwLyUpYmV2ZWxsZWRHRjRGam4tRj82MFEifkYnRjJGQkY4RjtGREZGRkhGSkZMRk5GUEZeby9GVkZfb0Zlb0ZqbkZmcC1GY282KC1GZ242J1EiM0YnRjJGQkY4RjtGaG9GXXBGX3BGYnBGZHBGam5Gam9Gam4tRj82MFEjLi5GJ0YyRkJGOEY7RkRGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRidGaXAtRj82MFEiLkYnRjJGQkY4RjtGREZGRkhGSkZMRk5GUEZeb0ZpcEYyRkJGMkZCRjhGOy8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRictRiw2I1EhRidGMkZC, the spectrum for a spinless hydrogen atom is 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<Text-field style="Heading 1" layout="Heading 1">Conclusions</Text-field>In this presentation, we derived, step-by-step, the SO(4) symmetry of the hydrogen atom and its spectrum using the computer algebra Maple system. The derivation was performed without departing from the results, entering only the main definition formulas in eqs. , and , followed by using a few simplification commands - mainly Simplify, SortProducts and SubstituteTensor - and a handful of Maple basic commands, subs, lhs, rhs and isolate. The computational path that was used to get the results of sections 2 to 8 is not unique. Instead of searching for the shortest path, we prioritized clarity and illustration of the techniques that can be used to work on problems like this one.
This problem is mainly about simplifying expressions using two different techniques. First, expressions with noncommutative operands in products need reduction with respect to the commutator algebra rules that have been set. Second, products of tensorial operators require simplification using the sum rule for repeated indices and the symmetries of tensorial subexpressions. Those techniques, which are part of the Maple Physics simplifier, together with the SortProducts and SubstituteTensor commands for sorting the operands in products to apply tensorial identities, sufficed. The derivations were performed in a reasonably small number of steps.
Two different computational strategies - with and without differential operators - were used in sections 3 and 5, showing a way to verify results, a relevant issue in general when performing complicated algebraic manipulations. The Maple Physics' ability to handle differential operators as noncommutative operands in products (as frequently done in paper and pencil computations) facilitates readability and ease in entering the computations. The complexity of those operations is then handled by one Physics:-Library command, ApplyProductsOfDifferentialOperators (see eqs. and ).
It is interesting to note: a) the ability of the system to factor expressions involving products of noncommutative operands (see eqs. and ) and b) the adaptation of the algorithms for simplifying tensorial expressions [6] to the noncommutativity domain, used throughout this presentation.
Also worth mentioning, the use of equation labels can reduce the whole computation to entering the main definitions, followed by applying a few commands to equation labels. That approach helps to reduce the chance of typographical errors to a very strict minimum. Likewise, the fact that commands and equations distribute over each other allows cumbersome manipulations to be performed in simple ways, as done, for instance, in eqs. , and . Additionally, it was helpful to have the display of each intermediate result automatically expressed using standard mathematical physics notation.Finally, if this work focused on a well-known case, the employed tools can be used to tackle a wide range of hot topics research in the quantum mechanics field, and beyond. To give but a few examples, recently (work in progress - see related Mapleprimes post [7]), we reproduced the calculus performed in [8]. This paper evaluates the constraints of magnetostatic traps for neutral cold atoms and Bose Einstein condensates. Besides, the overall possibilities includes the general framework of periodically driven systems, notably requiring Taylor development to approximate commutators [9]. The calculus could be extended to Lie superalgebra in the field of Anderson localization for disordered media, see [10] and supplemental material. Note that the present calculus is performed using an Euclidean metric. This feature could however easily be extended to any arbitrary metric, opening-up a wide range of possibilities to what can now be done with a computer, replacing pencil and paper.<Text-field style="Heading 1" layout="Heading 1">Acknowledgements</Text-field>This work was partly supported by the French Ministry of Higher Education and Research, Hauts-de-France Regional Council and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-Region (CPER Photonics for Society, P4S).<Text-field style="Heading 1" layout="Heading 1">Appendix</Text-field>In this presentation, the input lines are preceded by a promptLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiPkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRUYvRjI= and the commands used are of three kinds: some basic Maple manipulation commands, the main Physics package commands to set the context of a formulation and simplify expressions, and two commands of the Physics:-Library to perform specialized operations in expressions.The basic Maple commands usedinterface is used once at the beginning to set the letter used to represent the imaginary unit (default is I but we used i).isolate is used in several places to isolate a variable in an expression, for example isolating x in 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 results in 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lhs and rhs respectively get the left-hand side LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn and right-hand side LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn of an equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJCRidGL0YyRjVGMkY8subs substitutes the left-hand side of an equation by the right-hand side in a given target, for example 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 results in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUSJCRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUScmcGx1cztGJ0Y3L0Y7USdub3JtYWxGJy8lJmZlbmNlR0Y5LyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlMtRiw2JlEiQ0YnRjRGN0Y6RjdGQUYrRjdGQQ==@ is used to compose commands. So (A@B)(x)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 is the same as 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. This command is useful to express an abstract combo of manipulations, for example as in 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.The Physics commands usedSetup is used to set algebra rules as well as the dimension of space, type of metric, and conventions such as the kind of letter used to represent indices.Commutator computes the commutator between two objects using the algebra rules set using Setup. If no rules are known to the system, it outputs a representation for the commutator whose basic mathematical properties (expansion, differentiation and simplification) are known by the system.CompactDisplay is used to avoid redundant display of the functionality of a function.The input LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUSNkX0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNiUtRiw2JlEibkYnRjRGN0Y6RjcvRjtRJ25vcm1hbEYnRjdGRS8lJW9wZW5HUScmbHNxYjtGJy8lJmNsb3NlR1EnJnJzcWI7RidGN0ZFL0krbXNlbWFudGljc0dGJFEnYXRvbWljRidGK0Y3RkU= represents the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1ErJlBhcnRpYWxEO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEqUGh5c2ljc2RfRictRi82JlEibkYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= tensorial differential operator.Define is used to define tensors, with or without specifying its components.Dagger computes the Hermitian transpose of an expression.Normal, Expand, Factor respectively normalizes, expands and factorizes expressions that involve products of noncommutative operands.Simplify performs simplification of tensorial expressions involving products of noncommutative factors taking into account Einstein's sum rule for repeated indices, symmetries of the indices of tensorial subexpressions and custom commutator algebra rules.SortProducts uses the commutation rules set using Setup to sort the non-commutative operands of a product in an indicated ordering.SubstituteTensor substitutes the left-hand side of a tensorial equation, possibly a sum or a product of tensors, by its right-hand side, in a target tensorial expression. The substitution is performed taking the indices as parameters and automatically resolving potential collisions of free or repeated indices. SubstituteTensorIndices substitutes tensor indices (represented by letters of some kind) by other other tensor indices in a tensorial expression, taking care of not substituting occurrences of those same letters when they appear in the expression not as tensor indices.The Physics:-Library commands usedLibrary:-ApplyProductsOfDifferentialOperators applies the differential operators found in a product to the product operands that appear to its right. For example, applying this command to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJWRidGL0YyRjUtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJYRidGL0YyRjVGMkY8RjJGPC1GOTYuUTEmSW52aXNpYmxlVGltZXM7RidGMkY8Rj5GQEZCRkRGRkZIRkpGTEZPLUklbXN1YkdGJDYmLUYsNiZRIm1GJ0YvRjJGNS1GLDYmUSJlRidGL0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUYsNiNRIUYnRjJGPA== results in 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Library:-EqualizeRepeatedIndices equalizes the repeated indices in the terms of a sum, so for instance applying this command to 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 results in 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<Text-field style="Heading 1" layout="Heading 1">References</Text-field>[1] W. Pauli, "On the hydrogen spectrum from the standpoint of the new quantum mechanics,\342\200\235 Z. Phys. 36, 336\342\200\223363 (1926)[2] S. Weinberg, "Lectures on Quantum Mechanics, second edition," Cambridge University Press, 2015.[3] R. Gilmore, "Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists," Cambridge University Press, 2008.[4] Veronika G\303\241likov\303\241, Samuel Kov\303\241\304\215ik, and Peter Pre\305\241najder, "Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space", J. Math. Phys. 54, 122106 (2013)[5] Castro, P.G., Kullock, R. "Physics of the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEjc29GJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYvNiZRInFGJ0YyRjVGOEYyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiUtRiM2JS1JI21uR0YkNiVRIjRGJ0Y1L0Y5USdub3JtYWxGJ0Y1Rk9GNUZPRjVGTw== hydrogen atom". Theor. Math. Phys. 185, 1678\342\200\2231684 (2015).[6] L. R. U. Manssur, R. Portugal, and B. F. Svaiter, "Group-Theoretic Approach for Symbolic Tensor Manipulation," International Journal of Modern Physics C 13, 859-879 (2002).[7] P. Szriftgiser, E. S. Cheb-Terrab, Magnetic traps in cold-atom physics (2017).[8] R. Gerritsma, R. J. C. Spreeuw, "Topological constraints on magnetostatic traps," Phys. Rev. A 74, 043405 (2006).[9] N. Goldman and J. Dalibard, "Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields," Phys. Rev. X 4, 031027 (2014).[10] E. Khalaf, P. M. Ostrovsky, "Localization Effects on Magnetotransport of a Disordered Weyl Semimetal," Phys. Rev. Lett. 119, 106601 (2017).