Solving the 1-, 2-, and 3-dimensional Schrödinger equation for multiminima potentials using the Numerov-Cooley method. An extrapolation formula for energy eigenvalues (Q1122969)
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scientific article; zbMATH DE number 4108119
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving the 1-, 2-, and 3-dimensional Schrödinger equation for multiminima potentials using the Numerov-Cooley method. An extrapolation formula for energy eigenvalues |
scientific article; zbMATH DE number 4108119 |
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Solving the 1-, 2-, and 3-dimensional Schrödinger equation for multiminima potentials using the Numerov-Cooley method. An extrapolation formula for energy eigenvalues (English)
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1989
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The Numerov-Cooley algorithm is applied to solve the Schrödinger equation for multiminima potentials that, however, do not cause any stability problems. By means of the Richardson extrapolation formula an additional accuracy of the energy eigenvalues is obtained. The eigenfunctions corresponding to 1-dimensional potentials are used as basis functions for a perturbed 2-dimensional multiminima potential. Several numerical examples are presented, e.g. 2-dimensional case with 63-minima potential. FORTRAN 77 is used, some calculations being performed by means of REDUCE language.
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Numerov-Cooley algorithm
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Schrödinger equation
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multiminima potentials
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Richardson extrapolation
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energy eigenvalues
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eigenfunctions
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numerical examples
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