Quantum Mechanics: New Applications
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en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 23 Jan 2017 08:39:44 GMTMon, 23 Jan 2017 08:39:44 GMTNew applications in the Quantum Mechanics categoryhttp://www.mapleprimes.com/images/mapleapps.gifQuantum Mechanics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=184
Ground state of a quantum system of identical boson particles
http://www.maplesoft.com/applications/view.aspx?SID=154156&ref=Feed
Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154156/quantum.jpg" alt="Ground state of a quantum system of identical boson particles" align="left"/>Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.154156Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabThe Gross-Pitaevskii equation and Bogoliubov spectrum
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The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154155/theoreticalphysics.jpg" alt="The Gross-Pitaevskii equation and Bogoliubov spectrum" align="left"/>The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.154155Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantization of the Lorentz Force
http://www.maplesoft.com/applications/view.aspx?SID=154168&ref=Feed
Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154168/quantum.jpg" alt="Quantization of the Lorentz Force" align="left"/>Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.154168Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantum Mechanics: Schrödinger vs Heisenberg picture
http://www.maplesoft.com/applications/view.aspx?SID=154153&ref=Feed
Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154153/theoreticalphysicsThumb.jpg" alt="Quantum Mechanics: Schrödinger vs Heisenberg picture" align="left"/>Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
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This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.154153Thu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabThe Landau criterion for Superfluidity
http://www.maplesoft.com/applications/view.aspx?SID=154154&ref=Feed
The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.<img src="/view.aspx?si=154154/quantummechanics.jpg" alt="The Landau criterion for Superfluidity" align="left"/>The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.154154Thu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabMatrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation
http://www.maplesoft.com/applications/view.aspx?SID=154100&ref=Feed
In 1935, Einstein, Podolsky and Rosen published a paper revealing a counter-intuitive situation in quantum mechanics which was later known as the EPR paradox. The phenomenon involved an entangled state., which Schrodinger called "not one but the characteristic trait of quantum mechanics." In textbooks, entanglement is often presented in abstract notations. In popular accounts of quantum mechanics, entanglement is sometimes portrayed as a mystery or even distorted in a nearly pseudoscientific fashion. In this worksheet, we use Maple's LinearAlgebra package to represent quantum states and measurements in matrix form. The famous Bell's inequality and teleportation can be understood using elementary matrix operations.<img src="/view.aspx?si=154100/8df7b465a1583cedab7e3e6452644591.gif" alt="Matrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation" align="left"/>In 1935, Einstein, Podolsky and Rosen published a paper revealing a counter-intuitive situation in quantum mechanics which was later known as the EPR paradox. The phenomenon involved an entangled state., which Schrodinger called "not one but the characteristic trait of quantum mechanics." In textbooks, entanglement is often presented in abstract notations. In popular accounts of quantum mechanics, entanglement is sometimes portrayed as a mystery or even distorted in a nearly pseudoscientific fashion. In this worksheet, we use Maple's LinearAlgebra package to represent quantum states and measurements in matrix form. The famous Bell's inequality and teleportation can be understood using elementary matrix operations.154100Mon, 09 May 2016 04:00:00 ZDr. Frank WangDr. Frank WangOrbitals Package
http://www.maplesoft.com/applications/view.aspx?SID=4865&ref=Feed
The Orbitals package evaluates, plots and calculates atomic orbitals, overlap integrals, and atomic four-electron integrals for hydrogenic or Slater-type orbitals. This is an update of an earlier 2007 version.<img src="/view.aspx?si=4865/orbits.jpg" alt="Orbitals Package" align="left"/>The Orbitals package evaluates, plots and calculates atomic orbitals, overlap integrals, and atomic four-electron integrals for hydrogenic or Slater-type orbitals. This is an update of an earlier 2007 version.4865Tue, 06 Jan 2015 05:00:00 ZDavid HarringtonDavid HarringtonSimulation of a five qubits convolutional code
http://www.maplesoft.com/applications/view.aspx?SID=142318&ref=Feed
We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer. The encoding and decoding circuits and an error correction procedure are presented. We will verify that if any X, Y, Z error or any product of them occurs on one or two qubit, this correction always allows to recover the useful information or to obtain a list of possible errors. The originality in this correction is the winning time obtained by measuring only the required syndromes, thus avoiding the decoherence phenomenon. Also, we give the average fidelity for double errors recovered as single errors having same syndrome.<img src="/applications/images/app_image_blank_lg.jpg" alt="Simulation of a five qubits convolutional code" align="left"/>We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer. The encoding and decoding circuits and an error correction procedure are presented. We will verify that if any X, Y, Z error or any product of them occurs on one or two qubit, this correction always allows to recover the useful information or to obtain a list of possible errors. The originality in this correction is the winning time obtained by measuring only the required syndromes, thus avoiding the decoherence phenomenon. Also, we give the average fidelity for double errors recovered as single errors having same syndrome.142318Wed, 16 Jan 2013 05:00:00 ZFatiha MerazkaFatiha MerazkaDensity of Probability of an Electron near the Nucleus
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<p>In many situations is necesary to calculate the density of probability to find an electron near the nucleus. In this short article we calculate such probabilities in order to avoid the calculations and simplifications behind the problem. Due to the purpose of this article I will only expose the method to get the result for the s orbitals. The calculations can be easily arranged to produce the same results for other types of orbitals such as the p or d orbitals.<br /><br /></p><img src="/view.aspx?si=95272/95272.png" alt="Density of Probability of an Electron near the Nucleus" align="left"/><p>In many situations is necesary to calculate the density of probability to find an electron near the nucleus. In this short article we calculate such probabilities in order to avoid the calculations and simplifications behind the problem. Due to the purpose of this article I will only expose the method to get the result for the s orbitals. The calculations can be easily arranged to produce the same results for other types of orbitals such as the p or d orbitals.<br /><br /></p>95272Tue, 20 Jul 2010 04:00:00 ZDaniel Alonso HerculesDaniel Alonso HerculesSimulated Reality Hologram Matrix State Space (click-through calibration check)
http://www.maplesoft.com/applications/view.aspx?SID=95142&ref=Feed
<p>Free PDF:</p>
<p><a href="http://consc.net/online/8.3a">Simulated Reality Hologram Matrix State Space</a></p>
<p>Abstract</p>
<p>New holographic principle approach achieves spacetime, gravitational, electromagnetic uniﬁcation via Maxwell-Einstein gravitoelectromagnetic total stress energy (mass) density tensor Hilbert (4D ± 4Di) hologram interference ﬁeld stationary state domain of universal wave function. S-matrix in-states/out-states eigenvalue range, features (moment of inertia x angular velocity) <strong>SO</strong>(1, 3)<sub>ij</sub> self-adjoint operator integrations, generating Dirac-Noether conserved angular momentum observables in <em>material coordinates</em>. Fundamental quantum continuum equation returns gravitoelectromagnetic spectrum photon <strong>SO</strong>(1, 3)<sub>yy</sub> principle spin axis eigenvalues in units of Maxwell stress tensor pascals. New origin of electron-positron wave-particle mass-charge via energization of <strong>SO</strong>(1, 3)<sub>zz</sub> principle spin axis angular momentum, invariant throughout inertial dynamics of electromagnetic and gravitational ﬁelds being inversely compressive/dispersive of cosmological constant vacuum energy density tensor pressure, according to principle quantum number <em>n</em>. In thought experiment test vs. general theory via <em>pp</em>-waves microlensing problem, wherein light-to-light gravitational attraction is four times matter-to-matter attraction, hypothesis predicts null microlensing result in area general theory known to break down on microscopic scale.</p><img src="/view.aspx?si=95142/278203\SRHMSScalSpin2.gif" alt="Simulated Reality Hologram Matrix State Space (click-through calibration check)" align="left"/><p>Free PDF:</p>
<p><a href="http://consc.net/online/8.3a">Simulated Reality Hologram Matrix State Space</a></p>
<p>Abstract</p>
<p>New holographic principle approach achieves spacetime, gravitational, electromagnetic uniﬁcation via Maxwell-Einstein gravitoelectromagnetic total stress energy (mass) density tensor Hilbert (4D ± 4Di) hologram interference ﬁeld stationary state domain of universal wave function. S-matrix in-states/out-states eigenvalue range, features (moment of inertia x angular velocity) <strong>SO</strong>(1, 3)<sub>ij</sub> self-adjoint operator integrations, generating Dirac-Noether conserved angular momentum observables in <em>material coordinates</em>. Fundamental quantum continuum equation returns gravitoelectromagnetic spectrum photon <strong>SO</strong>(1, 3)<sub>yy</sub> principle spin axis eigenvalues in units of Maxwell stress tensor pascals. New origin of electron-positron wave-particle mass-charge via energization of <strong>SO</strong>(1, 3)<sub>zz</sub> principle spin axis angular momentum, invariant throughout inertial dynamics of electromagnetic and gravitational ﬁelds being inversely compressive/dispersive of cosmological constant vacuum energy density tensor pressure, according to principle quantum number <em>n</em>. In thought experiment test vs. general theory via <em>pp</em>-waves microlensing problem, wherein light-to-light gravitational attraction is four times matter-to-matter attraction, hypothesis predicts null microlensing result in area general theory known to break down on microscopic scale.</p>95142Thu, 15 Jul 2010 04:00:00 ZDavid HarnessDavid HarnessSimulation on maple of the nine qubit Shor code using Feynman program
http://www.maplesoft.com/applications/view.aspx?SID=34917&ref=Feed
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<p align="left">To simulate the evolution and behavior of an n-qubits system, a quantum simulator within the framework of the computer algebra system Maple called Feynman program has been built by S.Fritzsche and T.Radtke. In this work we use this program to implement the nine qubit Shor quantum error correcting code on a classical computer . We will present the encoding and decoding circuits and describe the error correction procedure using the Shor code gen-erators. We will verify that if any X, Y or Z error occur on any single qubit this correction procedure always allow to recover the usuful information. More-over, it permit at the end to put all the ancillas in the initial state and then too use them again. The simulation permit also the decoding without correction to measure all the output errors and know something about the canal transmitting the information.</p>
</span></span></span></p><img src="/view.aspx?si=34917//applications/images/app_image_blank_lg.jpg" alt="Simulation on maple of the nine qubit Shor code using Feynman program" align="left"/><p><span id="ctl00_mainContent__documentViewer"><span><span class="body summary">
<p align="left">To simulate the evolution and behavior of an n-qubits system, a quantum simulator within the framework of the computer algebra system Maple called Feynman program has been built by S.Fritzsche and T.Radtke. In this work we use this program to implement the nine qubit Shor quantum error correcting code on a classical computer . We will present the encoding and decoding circuits and describe the error correction procedure using the Shor code gen-erators. We will verify that if any X, Y or Z error occur on any single qubit this correction procedure always allow to recover the usuful information. More-over, it permit at the end to put all the ancillas in the initial state and then too use them again. The simulation permit also the decoding without correction to measure all the output errors and know something about the canal transmitting the information.</p>
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http://www.maplesoft.com/applications/view.aspx?SID=4976&ref=Feed
Scattering problem of quantum particles by the one-dimensional potential step is solved in MAPLE. Analytical formulas for reflection and transmission coefficients are obtained and visualized.<img src="/view.aspx?si=4976/QNT_STP_78.gif" alt="QUANTUM SCATTERING BY THE ONE-DIMENSIONAL POTENTIAL STEP IN MAPLE" align="left"/>Scattering problem of quantum particles by the one-dimensional potential step is solved in MAPLE. Analytical formulas for reflection and transmission coefficients are obtained and visualized.4976Wed, 30 May 2007 00:00:00 ZDr. Alexei TikhonenkoDr. Alexei Tikhonenko3j Coefficients and Coefficients of Russell-Saunders Interaction
http://www.maplesoft.com/applications/view.aspx?SID=4896&ref=Feed
3j coefficient calculator and related ak and bk coefficients for the residual electrostatic interaction. Used in Atomic Physics.
Acknowledgments: AM Sudupe ,F Ruiz Ruiz & M Ortiz, for their lessons.<img src="/view.aspx?si=4896//applications/images/app_image_blank_lg.jpg" alt="3j Coefficients and Coefficients of Russell-Saunders Interaction" align="left"/>3j coefficient calculator and related ak and bk coefficients for the residual electrostatic interaction. Used in Atomic Physics.
Acknowledgments: AM Sudupe ,F Ruiz Ruiz & M Ortiz, for their lessons.4896Mon, 16 Apr 2007 00:00:00 ZJuan TorresJuan TorresPX: A package for multiplication and commutation of quantum operators
http://www.maplesoft.com/applications/view.aspx?SID=4812&ref=Feed
PX is a Maple package designed to implement non-commutative multiplication and commutation of quantum operators. In particular it is designed to deal with systems with several degree of freedom satisfying the commutation relations of operators and their conjugate momenta; i.e., operators such as p[x] and x, or alternatively their associated annihilation and creation operators.<img src="/view.aspx?si=4812//applications/images/app_image_blank_lg.jpg" alt="PX: A package for multiplication and commutation of quantum operators" align="left"/>PX is a Maple package designed to implement non-commutative multiplication and commutation of quantum operators. In particular it is designed to deal with systems with several degree of freedom satisfying the commutation relations of operators and their conjugate momenta; i.e., operators such as p[x] and x, or alternatively their associated annihilation and creation operators.4812Mon, 28 Aug 2006 00:00:00 ZDr. Marvin WeinsteinDr. Marvin WeinsteinQuantum Grover`s algorithm
http://www.maplesoft.com/applications/view.aspx?SID=1448&ref=Feed
The Grover algorithm is a realization of quantum advantages, which we can use in the "search task". This is quantum algorithm for quantum computer, and it is difficulty to realize such algorithm with the ordinary machine. However, also with a power of the personal computer we can give some common image of the algorithm.<img src="/view.aspx?si=1448/Grover_64.gif" alt="Quantum Grover`s algorithm" align="left"/>The Grover algorithm is a realization of quantum advantages, which we can use in the "search task". This is quantum algorithm for quantum computer, and it is difficulty to realize such algorithm with the ordinary machine. However, also with a power of the personal computer we can give some common image of the algorithm.1448Fri, 18 Mar 2005 00:00:00 ZProf. Andrey TsiganovProf. Andrey TsiganovHydrogen 3D Contours
http://www.maplesoft.com/applications/view.aspx?SID=4329&ref=Feed
This worksheet demonstrates the use of Maple for calculating and displaying 3D contour plots of various hydrogen atomic orbitals and probability density of your choice.
This can be used in the area of physics,chemistry,quantum mechanics application. It illustrates how hydrogen atomic orbitals can be computed and displayed in 3D.<img src="/view.aspx?si=4329//applications/images/app_image_blank_lg.jpg" alt="Hydrogen 3D Contours" align="left"/>This worksheet demonstrates the use of Maple for calculating and displaying 3D contour plots of various hydrogen atomic orbitals and probability density of your choice.
This can be used in the area of physics,chemistry,quantum mechanics application. It illustrates how hydrogen atomic orbitals can be computed and displayed in 3D.4329Fri, 01 Nov 2002 10:40:28 ZProf. Takao TakeuchiProf. Takao TakeuchiPackage for the calculation of trace of Dirac gamma matrices
http://www.maplesoft.com/applications/view.aspx?SID=4306&ref=Feed
Main purpose of this package is to provide physicists by possibility to calculate gamma matrices traces using Maple (7.0) system.<img src="/view.aspx?si=4306//applications/images/app_image_blank_lg.jpg" alt="Package for the calculation of trace of Dirac gamma matrices" align="left"/>Main purpose of this package is to provide physicists by possibility to calculate gamma matrices traces using Maple (7.0) system.4306Tue, 17 Sep 2002 15:39:17 ZAndrea SiverAndrea SiverHydrogen Orbitals
http://www.maplesoft.com/applications/view.aspx?SID=4302&ref=Feed
This worksheet demonstrates the use of Maple for calculating H-orbitals for various quantum numbers (total, angular and magnetic). The result is shown as a contour plot using a Maplet with sliders for the quantum numbers.<img src="/view.aspx?si=4302/hydrogen.gif" alt="Hydrogen Orbitals" align="left"/>This worksheet demonstrates the use of Maple for calculating H-orbitals for various quantum numbers (total, angular and magnetic). The result is shown as a contour plot using a Maplet with sliders for the quantum numbers.4302Wed, 11 Sep 2002 16:53:44 ZMichael KommaMichael KommaThe ScientificConstants Package
http://www.maplesoft.com/applications/view.aspx?SID=4260&ref=Feed
The new ScientificConstants package in Maple 8 provides the values, symbols, uncertainty and units of over 13,000 physical constants. Never again do you have to search the internet or grab a reference book to look up such values. This extensive package gives you access to the basic chemical properties of any element or isotope from the Periodic Table. Also available are 70 physical constants, such as Planck's constant, the Newtonian constant of gravitation, magnetic flux quantum, and speed of light in a vacuum. If a specific physical constant that you need is not included, simply add the constants you commonly use to Maple's database. This flexible package also allows you to modify properties or change the system associated with a constant. The ScientificConstants package in conjunction with the comprehensive Units package introduced in Maple 7 together provide valuable tools for scientists and engineers.<img src="/view.aspx?si=4260//applications/images/app_image_blank_lg.jpg" alt="The ScientificConstants Package" align="left"/>The new ScientificConstants package in Maple 8 provides the values, symbols, uncertainty and units of over 13,000 physical constants. Never again do you have to search the internet or grab a reference book to look up such values. This extensive package gives you access to the basic chemical properties of any element or isotope from the Periodic Table. Also available are 70 physical constants, such as Planck's constant, the Newtonian constant of gravitation, magnetic flux quantum, and speed of light in a vacuum. If a specific physical constant that you need is not included, simply add the constants you commonly use to Maple's database. This flexible package also allows you to modify properties or change the system associated with a constant. The ScientificConstants package in conjunction with the comprehensive Units package introduced in Maple 7 together provide valuable tools for scientists and engineers.4260Mon, 15 Apr 2002 16:08:32 ZMaplesoftMaplesoftMultiple Quantum Filtered Spectra
http://www.maplesoft.com/applications/view.aspx?SID=3854&ref=Feed
Multiple Quantum Filtered Spectra - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence.<img src="/view.aspx?si=3854//applications/images/app_image_blank_lg.jpg" alt="Multiple Quantum Filtered Spectra" align="left"/>Multiple Quantum Filtered Spectra - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence.3854Wed, 20 Jun 2001 00:00:00 ZRene KantersRene Kanters