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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| Format: | Thesis |
| Language: | English English |
| Published: |
2003
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| Online Access: | http://psasir.upm.edu.my/id/eprint/9604/ http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf |
| _version_ | 1848841191509983232 |
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| author | Siddig, Abubaker Ahmed Mohamed |
| author_facet | Siddig, Abubaker Ahmed Mohamed |
| author_sort | Siddig, Abubaker Ahmed Mohamed |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T07:39:19Z |
| format | Thesis |
| id | upm-9604 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:39:19Z |
| publishDate | 2003 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Schrödinger equation. Quantum theory. Mathematics - Data processing. Siddig, Abubaker Ahmed Mohamed Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials |
| title | 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_short | Mathematica Packages for Solving Schrodinger Equation with One Dimensional Rectangular Potentials |
| title_sort | mathematica packages for solving schrodinger equation with one dimensional rectangular potentials |
| topic | Schrödinger equation. Quantum theory. Mathematics - Data processing. |
| url | http://psasir.upm.edu.my/id/eprint/9604/ http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf |