Quantum Mechanics: New Applications
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en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 01 Oct 2020 17:03:47 GMTThu, 01 Oct 2020 17:03:47 GMTNew applications in the Quantum Mechanics categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgQuantum Mechanics: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=165
Mathematics for Chemistry
https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=Feed
This interactive electronic textbook in the form of Maple worksheets comprises two parts.
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Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019<img src="https://www.maplesoft.com/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" style="max-width: 25%;" align="left"/>This interactive electronic textbook in the form of Maple worksheets comprises two parts.
<BR><BR>
Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
<BR><BR>
Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedTue, 30 May 2017 04:00:00 ZJohn OgilvieJohn OgilvieOrbitals Package
https://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="https://www.maplesoft.com/view.aspx?si=4865/orbits.jpg" alt="Orbitals Package" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4865&ref=FeedTue, 06 Jan 2015 05:00:00 ZDavid HarringtonDavid HarringtonThe Hydrogen Atom Orbitals
https://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="https://www.maplesoft.com/view.aspx?si=134917/1.jpg" alt="The Hydrogen Atom Orbitals" style="max-width: 25%;" 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>https://www.maplesoft.com/applications/view.aspx?SID=134917&ref=FeedFri, 08 Jun 2012 04:00:00 ZGiulio DujanyGiulio DujanyQUANTUM SCATTERING BY THE ONE-DIMENSIONAL POTENTIAL STEP IN MAPLE
https://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="https://www.maplesoft.com/view.aspx?si=4976/QNT_STP_78.gif" alt="QUANTUM SCATTERING BY THE ONE-DIMENSIONAL POTENTIAL STEP IN MAPLE" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4976&ref=FeedWed, 30 May 2007 00:00:00 ZDr. Alexei TikhonenkoDr. Alexei Tikhonenko3j Coefficients and Coefficients of Russell-Saunders Interaction
https://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="https://www.maplesoft.com/view.aspx?si=4896//applications/images/app_image_blank_lg.jpg" alt="3j Coefficients and Coefficients of Russell-Saunders Interaction" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4896&ref=FeedMon, 16 Apr 2007 00:00:00 ZJuan TorresJuan TorresPX: A package for multiplication and commutation of quantum operators
https://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="https://www.maplesoft.com/view.aspx?si=4812//applications/images/app_image_blank_lg.jpg" alt="PX: A package for multiplication and commutation of quantum operators" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4812&ref=FeedMon, 28 Aug 2006 00:00:00 ZDr. Marvin WeinsteinDr. Marvin WeinsteinQuantum Grover`s algorithm
https://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="https://www.maplesoft.com/view.aspx?si=1448/Grover_64.gif" alt="Quantum Grover`s algorithm" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=1448&ref=FeedFri, 18 Mar 2005 00:00:00 ZProf. Andrey TsiganovProf. Andrey TsiganovHydrogen 3D Contours
https://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="https://www.maplesoft.com/view.aspx?si=4329//applications/images/app_image_blank_lg.jpg" alt="Hydrogen 3D Contours" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4329&ref=FeedFri, 01 Nov 2002 10:40:28 ZProf. Takao TakeuchiProf. Takao TakeuchiPackage for the calculation of trace of Dirac gamma matrices
https://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="https://www.maplesoft.com/view.aspx?si=4306//applications/images/app_image_blank_lg.jpg" alt="Package for the calculation of trace of Dirac gamma matrices" style="max-width: 25%;" align="left"/>Main purpose of this package is to provide physicists by possibility to calculate gamma matrices traces using Maple (7.0) system.https://www.maplesoft.com/applications/view.aspx?SID=4306&ref=FeedTue, 17 Sep 2002 15:39:17 ZAndrea SiverAndrea SiverHydrogen Orbitals
https://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="https://www.maplesoft.com/view.aspx?si=4302/hydrogen.gif" alt="Hydrogen Orbitals" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4302&ref=FeedWed, 11 Sep 2002 16:53:44 ZMichael KommaMichael KommaThe ScientificConstants Package
https://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="https://www.maplesoft.com/view.aspx?si=4260//applications/images/app_image_blank_lg.jpg" alt="The ScientificConstants Package" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=4260&ref=FeedMon, 15 Apr 2002 16:08:32 ZMaplesoftMaplesoftGroundstate energy of Heisenberg model
https://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="https://www.maplesoft.com/view.aspx?si=3830//applications/images/app_image_blank_lg.jpg" alt="Groundstate energy of Heisenberg model" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=3830&ref=FeedWed, 20 Jun 2001 00:00:00 ZMarvin WeinsteinMarvin WeinsteinSmall-molecule program utilizing s-function basis sets II : MP2 Energies
https://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="https://www.maplesoft.com/view.aspx?si=3834//applications/images/app_image_blank_lg.jpg" alt="Small-molecule program utilizing s-function basis sets II : MP2 Energies" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=3834&ref=FeedWed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberHomonuclear A2MX one-dimensional spectrum
https://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="https://www.maplesoft.com/view.aspx?si=3855//applications/images/app_image_blank_lg.jpg" alt="Homonuclear A2MX one-dimensional spectrum " style="max-width: 25%;" align="left"/>Homonuclear A2MX one-dimensional spectrum - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence. https://www.maplesoft.com/applications/view.aspx?SID=3855&ref=FeedWed, 20 Jun 2001 00:00:00 ZRene KantersRene KantersDensity functional theory program for atoms utilizing s-function basis sets
https://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="https://www.maplesoft.com/view.aspx?si=3837//applications/images/app_image_blank_lg.jpg" alt="Density functional theory program for atoms utilizing s-function basis sets" style="max-width: 25%;" align="left"/>This application conveys a density functional theory program for atoms utilizing basis-sets consisting of s-functions (spherical Gaussians) only.
https://www.maplesoft.com/applications/view.aspx?SID=3837&ref=FeedWed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberHuckel molecular orbitals
https://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="https://www.maplesoft.com/view.aspx?si=3836//applications/images/app_image_blank_lg.jpg" alt="Huckel molecular orbitals" style="max-width: 25%;" align="left"/>Approximation of the electronic structure of molecules using the Huckel Molecular Orbital theory.https://www.maplesoft.com/applications/view.aspx?SID=3836&ref=FeedWed, 20 Jun 2001 00:00:00 ZDarren RedfernDarren RedfernCOSY spectrum of a Homonuclear AX Spinsystem
https://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="https://www.maplesoft.com/view.aspx?si=3852//applications/images/app_image_blank_lg.jpg" alt="COSY spectrum of a Homonuclear AX Spinsystem" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=3852&ref=FeedWed, 20 Jun 2001 00:00:00 ZRene KantersRene KantersOne-electron program utilizing s-function basis sets
https://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="https://www.maplesoft.com/view.aspx?si=3832//applications/images/app_image_blank_lg.jpg" alt="One-electron program utilizing s-function basis sets" style="max-width: 25%;" 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
https://www.maplesoft.com/applications/view.aspx?SID=3832&ref=FeedWed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter HuberMultiple Quantum Filtered Spectra
https://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="https://www.maplesoft.com/view.aspx?si=3854//applications/images/app_image_blank_lg.jpg" alt="Multiple Quantum Filtered Spectra" style="max-width: 25%;" align="left"/>Multiple Quantum Filtered Spectra - using product operator formalism for calculation & visualization of the effect of an NMR pulse sequence.https://www.maplesoft.com/applications/view.aspx?SID=3854&ref=FeedWed, 20 Jun 2001 00:00:00 ZRene KantersRene KantersSolution of the 1-D Schroedinger equation
https://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="https://www.maplesoft.com/view.aspx?si=3828//applications/images/app_image_blank_lg.jpg" alt="Solution of the 1-D Schroedinger equation" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=3828&ref=FeedWed, 20 Jun 2001 00:00:00 ZHanspeter HuberHanspeter Huber