SU(2) -- Monopole: Interbasis Expansion

TL;DR

This paper investigates a five-dimensional charge-dyon quantum system with an SU(2) monopole, solving the Schrödinger equation in different coordinate systems and deriving interbasis expansion coefficients using group theory.

Contribution

It provides a complete solution for the interbasis expansion of wave functions in a five-dimensional SU(2) monopole system, linking it to SU(2) Clebsch-Gordan coefficients.

Findings

Wave functions are separable in hyperspherical and parabolic coordinates.

Interbasis expansion coefficients are expressed via SU(2) Clebsch-Gordan coefficients.

The problem of interbasis expansion is fully solved.

Abstract

This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates. The problem of interbasis expansion of the wave functions is completely solved. The coefficients for the expansion of the parabolic basis in terms of the hyperspherical basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2).