Spheroidal analysis of the generalized MIC-Kepler system

Abstract

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.

12 pages

References in corpus (3)

• (Super)Oscillator on CP(N) and Constant Magnetic Field
• The generalized MIC-Kepler system
• The charge-dyon bound system in the spherical quantum well

Cited by in corpus (5)

• Relationship between quantum mechanics with and without monopoles
• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• 4D singular oscillator and generalized MIC-Kepler system
• The number radial coherent states for the generalized MICZ-Kepler problem
• Algebraic structure underlying spherical, parabolic and prolate spheroidal bases of the nine-dimensional MICZ-Kepler problem