The three-dimensional Dirac-Oscillator in the presence of Aharonov-Bohm and magnetic monopole potentials

TL;DR

This paper solves the Dirac equation with a three-dimensional Dirac-Oscillator potential in the presence of Aharonov-Bohm and magnetic monopole potentials, providing exact energy spectra and eigenfunctions.

Contribution

It presents exact solutions for the Dirac equation with a 3D Dirac-Oscillator and electromagnetic potentials, including Aharonov-Bohm and monopole effects, which is a novel analytical result.

Findings

Exact relativistic energy spectrum derived

Eigenfunctions explicitly obtained

Inclusion of Aharonov-Bohm and monopole potentials

Abstract

We study the Dirac equation in 3+1 dimensions with non-minimal coupling to isotropic radial three-vector potential and in the presence of static electromagnetic potential. The space component of the electromagnetic potential has angular (non-central) dependence such that the Dirac equation is completely separable in spherical coordinates. We obtain exact solutions for the case where the three-vector potential is linear in the radial coordinate (Dirac-Oscillator) and the time component of the electromagnetic potential vanishes. The relativistic energy spectrum and spinor eigenfunctions are obtained.