Quantum Mechanics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=165
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 19 Dec 2014 23:29:01 GMTFri, 19 Dec 2014 23:29:01 GMTNew applications in the Quantum Mechanics categoryhttp://www.mapleprimes.com/images/mapleapps.gifQuantum Mechanics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=165
The Hydrogen Atom Orbitals
http://www.maplesoft.com/applications/view.aspx?SID=134917&ref=Feed
<p>Almost a century after their modeling in quantum mechanics as wave functions, hydrogen's orbitals have become a common subject in High school and even previous degree of education. In this worksheet is shown as Maple provides useful tools for studying and visualizing the hydrogen's orbitals. In particular interactive components can provide a useful didactic aid easily generating and visualizing the wave functions, and different probability plots (radial, orbital).</p><img src="/view.aspx?si=134917/1.jpg" alt="The Hydrogen Atom Orbitals" align="left"/><p>Almost a century after their modeling in quantum mechanics as wave functions, hydrogen's orbitals have become a common subject in High school and even previous degree of education. In this worksheet is shown as Maple provides useful tools for studying and visualizing the hydrogen's orbitals. In particular interactive components can provide a useful didactic aid easily generating and visualizing the wave functions, and different probability plots (radial, orbital).</p>134917Fri, 08 Jun 2012 04:00:00 ZGiulio DujanyGiulio DujanyQUANTUM SCATTERING BY THE ONE-DIMENSIONAL POTENTIAL STEP IN MAPLE
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 TorresOrbitals Package
http://www.maplesoft.com/applications/view.aspx?SID=4865&ref=Feed
A package to manipulate and plot atomic orbitals and spherical harmonics. Hydrogenic and Slater-type orbitals are supported, as are arbitrary radial functions. Quantum mechanical integrals are included that act on these orbitals: 2-centre overlap integrals and 4-electron atomic integrals, including coulomb and exchange integrals.
Help pages and an example worksheet are included.
This is an update of a version of the orbitals package that was published in 2003.<img src="/view.aspx?si=4865/Orbitals_29.jpg" alt="Orbitals Package" align="left"/>A package to manipulate and plot atomic orbitals and spherical harmonics. Hydrogenic and Slater-type orbitals are supported, as are arbitrary radial functions. Quantum mechanical integrals are included that act on these orbitals: 2-centre overlap integrals and 4-electron atomic integrals, including coulomb and exchange integrals.
Help pages and an example worksheet are included.
This is an update of a version of the orbitals package that was published in 2003.4865Mon, 05 Feb 2007 00:00:00 ZProf. David HarringtonProf. David HarringtonPX: 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 WeinsteinRelativistic Medium From Unified Energy Vector
http://www.maplesoft.com/applications/view.aspx?SID=1765&ref=Feed
A photon is postulated to be a wavetrain having a coherence length equal to one wavelength. The wavepulse is analyzed for a unified flux distribution, in its own inertial frame, based on the symmetric addition to the Poynting-Heaviside energy vector S of a gravitational cross product, as an alternative to that first proposed by Heaviside. From the mutual restoring force of the cross products a relativistic medium emerges, wherein there is no string, presenting an alternative to string/M-theory.
Maple 10 is used to analyze the symmetric three dimensional electric, magnetic, and gravitational flux distribution of the quantum on a similar basis to static charged rest mass electron-proton flux distributions in their own inertial frame. Eddington's detection of the deflection of light by the sun, and Tolman's detection of a gravitational component to electromagnetic radiation, previously attributed to spacetime curvature, are re-interpreted. The quantum's spacecurve flux distribution is shown in pair production to gain a spin moment, an added degree of freedom, through the interaction with the field of a nuclei, enabling the spherical expansion of the quantum into the electron and positron flux configurations.
Please download the .zip file to get both worksheets for this application.<img src="/view.aspx?si=1765/thumb.jpg" alt="Relativistic Medium From Unified Energy Vector" align="left"/>A photon is postulated to be a wavetrain having a coherence length equal to one wavelength. The wavepulse is analyzed for a unified flux distribution, in its own inertial frame, based on the symmetric addition to the Poynting-Heaviside energy vector S of a gravitational cross product, as an alternative to that first proposed by Heaviside. From the mutual restoring force of the cross products a relativistic medium emerges, wherein there is no string, presenting an alternative to string/M-theory.
Maple 10 is used to analyze the symmetric three dimensional electric, magnetic, and gravitational flux distribution of the quantum on a similar basis to static charged rest mass electron-proton flux distributions in their own inertial frame. Eddington's detection of the deflection of light by the sun, and Tolman's detection of a gravitational component to electromagnetic radiation, previously attributed to spacetime curvature, are re-interpreted. The quantum's spacecurve flux distribution is shown in pair production to gain a spin moment, an added degree of freedom, through the interaction with the field of a nuclei, enabling the spherical expansion of the quantum into the electron and positron flux configurations.
Please download the .zip file to get both worksheets for this application.1765Thu, 20 Jul 2006 04:00:00 ZDavid HarnessDavid HarnessQuantum 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 ZMaplesoftMaplesoftGroundstate energy of Heisenberg model
http://www.maplesoft.com/applications/view.aspx?SID=3830&ref=Feed
The goal is to evaluate the core approximation formula for the groundstate energy density of a 1+1-dimensional Heisenberg antiferromagnet, based upon a single-state truncation procedure out to range-6 and see how well the basic cluster expansion converges and then, how it can be accelerated using type-II Pade approximants.<img src="/view.aspx?si=3830//applications/images/app_image_blank_lg.jpg" alt="Groundstate energy of Heisenberg model" align="left"/>The goal is to evaluate the core approximation formula for the groundstate energy density of a 1+1-dimensional Heisenberg antiferromagnet, based upon a single-state truncation procedure out to range-6 and see how well the basic cluster expansion converges and then, how it can be accelerated using type-II Pade approximants.3830Wed, 20 Jun 2001 00:00:00 ZMarvin WeinsteinMarvin WeinsteinSmall-molecule program utilizing s-function basis sets II : MP2 Energies
http://www.maplesoft.com/applications/view.aspx?SID=3834&ref=Feed
This application discusses a MP2-program for small molecules utilizing basis-sets consisting of s-functions (spherical Gaussians) only. For this example, data is read from file, which were generated by the ab initio SCF-program.<img src="/view.aspx?si=3834//applications/images/app_image_blank_lg.jpg" alt="Small-molecule program utilizing s-function basis sets II : MP2 Energies" align="left"/>This application discusses a MP2-program for small molecules utilizing basis-sets consisting of s-functions (spherical Gaussians) only. For this example, data is read from file, which were generated by the ab initio SCF-program.3834Wed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberHomonuclear A2MX one-dimensional spectrum
http://www.maplesoft.com/applications/view.aspx?SID=3855&ref=Feed
Homonuclear A2MX one-dimensional spectrum - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence. <img src="/view.aspx?si=3855//applications/images/app_image_blank_lg.jpg" alt="Homonuclear A2MX one-dimensional spectrum " align="left"/>Homonuclear A2MX one-dimensional spectrum - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence. 3855Wed, 20 Jun 2001 00:00:00 ZRene KantersRene KantersDensity functional theory program for atoms utilizing s-function basis sets
http://www.maplesoft.com/applications/view.aspx?SID=3837&ref=Feed
This application conveys a density functional theory program for atoms utilizing basis-sets consisting of s-functions (spherical Gaussians) only.
<img src="/view.aspx?si=3837//applications/images/app_image_blank_lg.jpg" alt="Density functional theory program for atoms utilizing s-function basis sets" align="left"/>This application conveys a density functional theory program for atoms utilizing basis-sets consisting of s-functions (spherical Gaussians) only.
3837Wed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberHuckel molecular orbitals
http://www.maplesoft.com/applications/view.aspx?SID=3836&ref=Feed
Approximation of the electronic structure of molecules using the Huckel Molecular Orbital theory.<img src="/view.aspx?si=3836//applications/images/app_image_blank_lg.jpg" alt="Huckel molecular orbitals" align="left"/>Approximation of the electronic structure of molecules using the Huckel Molecular Orbital theory.3836Wed, 20 Jun 2001 00:00:00 ZDarren RedfernDarren RedfernCOSY spectrum of a Homonuclear AX Spinsystem
http://www.maplesoft.com/applications/view.aspx?SID=3852&ref=Feed
The COSY spectrum of a homonuclear AX spinsystem - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence.<img src="/view.aspx?si=3852//applications/images/app_image_blank_lg.jpg" alt="COSY spectrum of a Homonuclear AX Spinsystem" align="left"/>The COSY spectrum of a homonuclear AX spinsystem - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence.3852Wed, 20 Jun 2001 00:00:00 ZRene KantersRene KantersOne-electron program utilizing s-function basis sets
http://www.maplesoft.com/applications/view.aspx?SID=3832&ref=Feed
Ab initio one-electron program for small molecules utilizing basis-sets consisting of s-functions (spherical Gaussians). In this example, there is 1 nucleus and 2 basis functions on the nucleus
<img src="/view.aspx?si=3832//applications/images/app_image_blank_lg.jpg" alt="One-electron program utilizing s-function basis sets" align="left"/>Ab initio one-electron program for small molecules utilizing basis-sets consisting of s-functions (spherical Gaussians). In this example, there is 1 nucleus and 2 basis functions on the nucleus
3832Wed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberMultiple 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 KantersSolution of the 1-D Schroedinger equation
http://www.maplesoft.com/applications/view.aspx?SID=3828&ref=Feed
Solution of the Schroedinger equation by the Numerov-method for any given one-dimensional eigenvalue problem is shown here. The central idea is to fix the eigenvalue and solve the differential equation. If the resulting function is not an eigenfunction, the deviation serves as a guide how to change the eigenvalue. Here follows an abstract of the theory.<img src="/view.aspx?si=3828//applications/images/app_image_blank_lg.jpg" alt="Solution of the 1-D Schroedinger equation" align="left"/>Solution of the Schroedinger equation by the Numerov-method for any given one-dimensional eigenvalue problem is shown here. The central idea is to fix the eigenvalue and solve the differential equation. If the resulting function is not an eigenfunction, the deviation serves as a guide how to change the eigenvalue. Here follows an abstract of the theory.3828Wed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter Huber