Exact solution of the Dirac equation for a Coulomb and a scalar Potential in the presence of of an Aharonov-Bohm and magnetic monopole fields

TL;DR

This paper derives exact solutions for the Dirac equation involving Coulomb, scalar, Aharonov-Bohm, and magnetic monopole fields, revealing how the energy spectrum depends on these potentials' strengths.

Contribution

It provides an exact algebraic solution to the Dirac equation with combined Coulomb, scalar, monopole, and Aharonov-Bohm fields, a novel comprehensive analysis.

Findings

Exact solutions for the Dirac equation in complex field configurations

Explicit energy spectrum dependence on Aharonov-Bohm and monopole parameters

Complete separation of variables in spherical coordinates

Abstract

In the present article we analyze the problem of a relativistic Dirac electron in the presence of a combination of a Coulomb field, a $1/r$ scalar potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential. Using the algebraic method of separation of variables, the Dirac equation expressed in the local rotating diagonal gauge is completely separated in spherical coordinates, and exact solutions are obtained. We compute the energy spectrum and analyze how it depends on the intensity of the Aharonov-Bohm and the magnetic monopole strengths.