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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| المؤلف الرئيسي: | |
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| التنسيق: | أطروحة |
| اللغة: | English English |
| منشور في: |
2003
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://psasir.upm.edu.my/id/eprint/9604/1/FSAS_2003_57_IR.pdf |
| الوسوم: |
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| الملخص: | 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. |
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