SPHEROIDAL BASIS OF THE GENERALIZED MIK-KEPLER PROBLEM

Abstract

Super integrated systems have an extremely important property: they allow the separation of variables in the Hamilton-Jacobi and Schrödinger equations in several orthogonal coordinate systems. The choice of a specific coordinate system is dictated by considerations of convenience, for example, the spectroscopic problem of hydrogen-like systems uses a spherical coordinate system, when considering the Stark effect - a parabolic coordinate system, and in the two-center problem - elongated spheroid coordinates. This abundance of separation of variables in the Schrödinger equation for super integrated systems leads to the problem of interphasic decompositions, i.e. there is a need to move from one wave function to another. The generalized MIC-Kepler problem in spherical coordinates is considered as an explicit form of the additional motion integral and the generalized MIC-Kepler problem in spheroid coordinates is given Λ ̂=M ̂+(R√(μ_0 ))/ℏ Ω ̂^((s) ) main function of which is the spheroid basis and three-membered recurrent relations are derived to which the decomposition coefficients of the spheroid basis according to spherical and parabolic bases as well.