dorsal/arxiv
View SchemaAn accurate spectral method for solving the Schroedinger equation
| Authors | G. H. Rawitscher, I. Koltracht |
|---|---|
| Categories | |
| ArXiv ID | physics/0203032 |
| URL | https://arxiv.org/abs/physics/0203032 |
Abstract
The solution of the Lippman-Schwinger (L-S) integral equation is equivalent to the the solution of the Schroedinger equation. A new numerical algorithm for solving the L-S equation is described in simple terms, and its high accuracy is confirmed for several physical situations. They are: the scattering of an electron from a static hydrogen atom in the presence of exchange, the scattering of two atoms at ultra low temperatures, and barrier penetration in the presence of a resonance for a Morse potential. A key ingredient of the method is to divide the radial range into partitions, and in each partition expand the solution of the L-S equation into a set of Chebyshev polynomials. The expansion is called "spectral" because it converges rapidly to high accuracy. Properties of the Chebyshev expansion, such as rapid convergence, are illustrated by means of a simple example.
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"abstract": "The solution of the Lippman-Schwinger (L-S) integral equation is equivalent\nto the the solution of the Schroedinger equation. A new numerical algorithm for\nsolving the L-S equation is described in simple terms, and its high accuracy is\nconfirmed for several physical situations. They are: the scattering of an\nelectron from a static hydrogen atom in the presence of exchange, the\nscattering of two atoms at ultra low temperatures, and barrier penetration in\nthe presence of a resonance for a Morse potential. A key ingredient of the\nmethod is to divide the radial range into partitions, and in each partition\nexpand the solution of the L-S equation into a set of Chebyshev polynomials.\nThe expansion is called \"spectral\" because it converges rapidly to high\naccuracy. Properties of the Chebyshev expansion, such as rapid convergence, are\nillustrated by means of a simple example.",
"arxiv_id": "physics/0203032",
"authors": [
"G. H. Rawitscher",
"I. Koltracht"
],
"categories": [
"physics.comp-ph",
"physics.atom-ph"
],
"title": "An accurate spectral method for solving the Schroedinger equation",
"url": "https://arxiv.org/abs/physics/0203032"
},
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