Nonrelativistic Quantum Analysis of the Charged Particle-Dyon System on a Conical Spacetime

TL;DR

This paper develops a nonrelativistic quantum framework for a charged particle-dyon system in a conical spacetime, revealing how topological defects and harmonic potentials alter energy spectra and wave functions.

Contribution

It introduces conical monopole harmonics for the first time, generalizing previous models to include cosmic string-induced conical geometries.

Findings

Derived explicit bound and scattering wave functions.

Analyzed the impact of topological defects on energy spectra.

Showed harmonic potentials significantly modify energy levels.

Abstract

In this paper we develop the nonrelativistic quantum analysis of the charged particle-dyon system in the spacetime produced by an idealized cosmic string. In order to do that, we assume that the dyon is superposed to the cosmic string. Considering this peculiar configuration {\it conical} monopole harmonics are constructed, which are a generalizations of previous monopole harmonics obtained by Wu and Yang(1976 {\it Nucl. Phys. B} {\bf 107} 365) defined on a conical three-geometry. Bound and scattering wave functions are explicitly derived. As to bound states, we present the energy spectrum of the system, and analyze how the presence of the topological defect modifies obtained result. We also analyze this system admitting the presence of an extra isotropic harmonic potential acting on the particle. We show that the presence of this potential produces significant changes in the energy spectrum of the system.