Systematic and intuitive approach for separation of variables in the Dirac equation for a class of noncentral electromagnetic potentials

TL;DR

This paper develops a systematic method for separating variables in the Dirac equation with noncentral electromagnetic potentials, providing exact solutions including Coulomb, Aharonov-Bohm, and magnetic monopole cases.

Contribution

It introduces a novel approach to solve the Dirac equation with noncentral potentials, yielding exact solutions under specific gauge and potential conditions.

Findings

Derived exact relativistic energy spectra.

Obtained explicit spinor wavefunctions.

Included solutions with Aharonov-Bohm and magnetic monopole potentials.

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. The conventional relativistic units, $\hbar$ = c = 1, are used.