广义MIC-Kepler系统的球面分析
Spheroidal analysis of the generalized MIC-Kepler system
摘要：
本文讨论了广义MIC-Kepler系统的动力系统。结果表明，该广义MIC-Kepler系统的薛定谔方程可以在长球坐标系中分离。详细研究了球面、抛物面和椭球面三种基间展开式的系数。我们发现抛物基的这种球基展开式的系数可以通过SU（2）群的Clebsch-Gordan系数来表示，反之亦然。证明了长椭球基的球基和抛物基展开式的系数满足三项递推关系。
英文摘要：
This paper deals with the dynamical system that generalizes the MIC-Kepler system. It is shown that the Schrödinger 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.
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