On a Generalized Kepler-Coulomb System: Interbasis Expansions

Details On a Generalized Kepler-Coulomb System: Interbasis Expansions On a Generalized Kepler-Coulomb System: Interbasis Expansions

1994-09-05

arxiv.org/abs/hep-th/9409033v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, Latex, LYCEN 9415

Scientific paper

This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schr\"odinger equation for this generalized Kepler-Coulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coefficients for the expansion of the parabolic basis in terms of the spherical basis, and vice-versa, can be expressed through the Clebsch-Gordan coefficients for the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the spherical and parabolic bases are proved to satisfy three-term recursion relations.

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