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Phase-amplitude method for numerically exact solution of the differential equations of the two-center Coulomb problem.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
2001 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, Vol. 43, no 5, 2169-2179 p.Article in journal (Refereed) Published
Abstract [en]

The Coulomb two-center problem has been thoroughly investigated with special emphasis on the ${\rm H}_2^+$ molecule. The authors use a generalization of the phase amplitude technique which was introduced by several authors in the 1930s for the solution of the one-particle Schrödinger equation. P. O. Fröman, K. Larsson and A. Hökback \ref[J. Math. Phys. 40 (1999), no. 4, 1764--1779; MR1683099 (2000c:81072)] extended the technique for multi-well potentials. The two-center Coulomb problem corresponds for small internuclear distances to a single-well problem and for large internuclear distances to a double-well problem. The generalized technique is discussed in an appendix, where also an error in the above-mentioned article is corrected. Numerical applications to the states $1s\sigma, 2p\sigma, 3d\pi, 5f\pi$ are compared to values in the literature for various nuclear distances. Though the phase amplitude technique is in principle numerically exact, numerical difficulties prevented a complete agreement with "numerical exact values". Unfortunately, these values are taken from internal reports without a description of the method. The authors give a selection of references, but important mathematical articles on the two-center problem, and some very high precision results, are lacking.

Place, publisher, year, edition, pages
2001. Vol. 43, no 5, 2169-2179 p.
Identifiers
URN: urn:nbn:se:uu:diva-21043DOI: doi:10.1063/1.1465098OAI: oai:DiVA.org:uu-21043DiVA: diva2:48816
Available from: 2006-12-18 Created: 2006-12-18 Last updated: 2011-01-13

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Fröman, Per Olof

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