  This paper deals with the dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler 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 this expansion of the parabolic basis in terms of the
spherical basis, and vice-versa, can be expresses 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 prolate spheroidal basis
in terms of the spherical and parabolic bases are proved to satisfy three-term
recursion relations.
