Solution of the Dirac equation with non-minimal coupling to noncentral three-vector potential

TL;DR

This paper extends the Dirac equation to include non-minimal, noncentral three-vector potentials, deriving the energy spectrum and wavefunctions for a specific radial potential, generalizing previous Dirac-oscillator models.

Contribution

It introduces a novel non-minimal coupling to noncentral potentials in the Dirac equation, enabling complete separation in spherical coordinates and analytical solutions.

Findings

Derived relativistic energy spectrum for the non-minimal coupling case

Obtained explicit spinor wavefunctions

Generalized the Dirac-oscillator model with noncentral potentials

Abstract

We introduce non-minimal coupling to three-vector potential in the 3+1 dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wavefunctions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The non-minimal coupling presented in this work is a generalization of that which was introduced by Moshinsky and Szczepaniak in the Dirac-Oscillator problem.