On a generalized Kepler–Coulomb system: Interbasis expansions

This article deals with a dynamical system that generalizes the Kepler–Coulomb system and the Hartmann system. It is shown that the Schrodinger 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 vica versa, can be expressed through the Clebsch–Gorden 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. © 1994 John Wiley & Sons, Inc.