Solution of the Dirac equation by separation of variables in spherical coordinates for a class of three-parameter non-central electromagnetic potential

TL;DR

This paper derives exact solutions for the Dirac equation in spherical coordinates with a specific class of non-central electromagnetic potentials, including Coulomb, Aharonov-Bohm, and magnetic monopole effects, expanding analytical understanding of relativistic quantum systems.

Contribution

It introduces a method to solve the Dirac equation with a three-parameter non-central potential, providing explicit energy spectra and wavefunctions under these conditions.

Findings

Exact relativistic energy spectrum obtained.

Wavefunctions explicitly derived for the potential class.

Inclusion of Aharonov-Bohm and magnetic monopole effects.

Abstract

We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is separable in all coordinates. We obtain exact solutions for the case where the potential satisfies the Lorentz gauge fixing condition and its time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wavefunctions are obtained. The Aharonov-Bohm and magnetic monopole potentials are included in these solutions.