Quadratic algebra for superintegrable monopole system in a Taub-NUT space

TL;DR

This paper introduces a superintegrable quantum system in a generalized Taub-NUT space with monopole interactions, deriving its algebraic structure and energy spectra, which unify several known monopole models.

Contribution

It constructs a quadratic algebra for the superintegrable monopole system in Taub-NUT space and links it to physical energy spectra, extending previous models.

Findings

Quadratic algebra and Casimir operator derived

Energy spectra obtained from algebraic and separation of variables methods

Unification of Kaluza-Klein and MIC-Zwanziger monopoles

Abstract

We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrodinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.