  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.
