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
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id	my-upm-ir.9604
record_format	uketd_dc
spelling	my-upm-ir.96042023-11-28T02:16:14Z Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials 2003-01 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. Schrödinger equation. Quantum theory. Mathematics - Data processing. 2003-01 Thesis http://psasir.upm.edu.my/id/eprint/9604/ http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf text en public masters Universiti Putra Malaysia Schrödinger equation. Quantum theory. Mathematics - Data processing. Faculty of Science and Environmental Studies Zainuddin, Hishamuddin English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
advisor	Zainuddin, Hishamuddin
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
qualification_level	Master's degree
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
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science and Environmental Studies
publishDate	2003
url	http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf
_version_	1794018853784649728

Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials

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