Quantal two-center Coulomb problem treated by means of the phase-integral method. I. General theory

Athavan, N. ; Froman, P. O. ; Froman, N. ; Lakshmanan, M. (2001) Quantal two-center Coulomb problem treated by means of the phase-integral method. I. General theory Journal of Mathematical Physics, 42 (11). pp. 5051-5076. ISSN 0022-2488

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Official URL: http://link.aip.org/link/?JMAPAQ/42/5051/1

Related URL: http://dx.doi.org/10.1063/1.1399294

Abstract

The present paper concerns the derivation of phase-integral quantization conditions for the two-center Coulomb problem under the assumption that the two Coulomb centers are fixed. With this restriction we treat the general two-center Coulomb problem according to the phase-integral method, in which one uses an a priori unspecified base function. We consider base functions containing three unspecified parameters C, C-, and Λ. When the absolute value of the magnetic quantum number m is not too small, it is most appropriate to choose Λ = |m| ≠ 0. When, on the other hand, |m| is sufficiently small, it is most appropriate to choose Λ = 0. Arbitrary-order phase-integral quantization conditions are obtained for these choices of Λ. The parameters C and C- are determined from the requirement that the results of the first and the third order of the phase-integral approximation coincide, which makes the first-order approximation as good as possible. In order to make the paper to some extent self-contained, a short review of the phase-integral method is given in the Appendix.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:19501
Deposited On:22 Nov 2010 12:30
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