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Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials

The determination of eigenvalues and their related eigenfunctions is one of the central problems of quantum mechanics. In this work, the problem of finding energy eigenvalues and eigenfunctions are aptly demonstrated with one dimensional systems of infinite double square well potential, finite do...

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Main Author: Siddig, Abubaker Ahmed Mohamed
Format: Thesis
Language:English
English
Published: 2003
Subjects:
Schrödinger equation.
Quantum theory.
Mathematics - Data processing.
Online Access:http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf
http://psasir.upm.edu.my/id/eprint/9604/
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spelling my.upm.eprints.96042023-11-28T02:16:14Z http://psasir.upm.edu.my/id/eprint/9604/ Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials Siddig, Abubaker Ahmed Mohamed The determination of eigenvalues and their related eigenfunctions is one of the central problems of quantum mechanics. In this work, the problem of finding energy eigenvalues and eigenfunctions are aptly demonstrated with one dimensional systems of infinite double square well potential, finite double square well potential, rectangular potential hole between two walls and asymmetric square well potential. We develop Mathematica packages for which the Schrodinger equations are solved for each model. The solutions are obtained by graphical and numerical methods in these packages. The packages are easy to use; the user does not need to know the details of the packages in order to use them but the user has a direct control over parameters of the models. Eigenvalues and eigenfunctions have been obtained for various well depths and widths as well as various barrier widths. They are shown to have appropriate limiting solutions. The packages are stable, fast, efficient and can serve as useful tools for teaching systems of one dimensional rectangular potential, in quantum mechanics. 2003-01 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf Siddig, Abubaker Ahmed Mohamed (2003) Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials. Masters thesis, Universiti Putra Malaysia. Schrödinger equation. Quantum theory. Mathematics - Data processing. English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
English
topic Schrödinger equation.
Quantum theory.
Mathematics - Data processing.
spellingShingle Schrödinger equation.
Quantum theory.
Mathematics - Data processing.
Siddig, Abubaker Ahmed Mohamed
Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
description The determination of eigenvalues and their related eigenfunctions is one of the central problems of quantum mechanics. In this work, the problem of finding energy eigenvalues and eigenfunctions are aptly demonstrated with one dimensional systems of infinite double square well potential, finite double square well potential, rectangular potential hole between two walls and asymmetric square well potential. We develop Mathematica packages for which the Schrodinger equations are solved for each model. The solutions are obtained by graphical and numerical methods in these packages. The packages are easy to use; the user does not need to know the details of the packages in order to use them but the user has a direct control over parameters of the models. Eigenvalues and eigenfunctions have been obtained for various well depths and widths as well as various barrier widths. They are shown to have appropriate limiting solutions. The packages are stable, fast, efficient and can serve as useful tools for teaching systems of one dimensional rectangular potential, in quantum mechanics.
format Thesis
author Siddig, Abubaker Ahmed Mohamed
author_facet Siddig, Abubaker Ahmed Mohamed
author_sort Siddig, Abubaker Ahmed Mohamed
title Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
title_short Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
title_full Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
title_fullStr Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
title_full_unstemmed Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials
title_sort mathematica packages for solving schrodinger equation with one dimensional rectangular potentials
publishDate 2003
url http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf
http://psasir.upm.edu.my/id/eprint/9604/
_version_ 1783879913730736128
score 13.211869

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