dorsal/arxiv
View SchemaA Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms
| Authors | G. H. Rawitscher, S. Y. Kang, I. Koltracht, E. Zerrad, K. Zerrad, B. T. Kim, T. Udagawa |
|---|---|
| Categories | |
| ArXiv ID | physics/0201066 |
| URL | https://arxiv.org/abs/physics/0201066 |
| DOI | 10.1063/1.1567254 |
Abstract
In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schroedinger Eq. of an integro-differential form. We describe a new spectral noniterative method (S-IEM), previously developed for solving the Lippman-Schwinger integral equation with local potentials, which has now been extended so as to include the exchange nonlocality. We apply it to the restricted case of electron-Hydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to three other methods. One is a non-iterative solution (NIEM) of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The third one is based on the Singular Value Decomposition of the exchange term followed by iterations over the remainder. The S-IEM method turns out to be more accurate by many orders of magnitude than any of the other three methods described above for the same number of mesh points.
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"abstract": "In the Hartree-Fock approximation the Pauli exclusion principle leads to a\nSchroedinger Eq. of an integro-differential form. We describe a new spectral\nnoniterative method (S-IEM), previously developed for solving the\nLippman-Schwinger integral equation with local potentials, which has now been\nextended so as to include the exchange nonlocality. We apply it to the\nrestricted case of electron-Hydrogen scattering in which the bound electron\nremains in the ground state and the incident electron has zero angular\nmomentum, and we compare the acuracy and economy of the new method to three\nother methods. One is a non-iterative solution (NIEM) of the integral equation\nas described by Sams and Kouri in 1969. Another is an iterative method\nintroduced by Kim and Udagawa in 1990 for nuclear physics applications, which\nmakes an expansion of the solution into an especially favorable basis obtained\nby a method of moments. The third one is based on the Singular Value\nDecomposition of the exchange term followed by iterations over the remainder.\nThe S-IEM method turns out to be more accurate by many orders of magnitude than\nany of the other three methods described above for the same number of mesh\npoints.",
"arxiv_id": "physics/0201066",
"authors": [
"G. H. Rawitscher",
"S. Y. Kang",
"I. Koltracht",
"E. Zerrad",
"K. Zerrad",
"B. T. Kim",
"T. Udagawa"
],
"categories": [
"physics.atom-ph",
"physics.comp-ph"
],
"doi": "10.1063/1.1567254",
"title": "A Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms",
"url": "https://arxiv.org/abs/physics/0201066"
},
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