Eigenfunctions of the two-dimensional Moshinsky-Szczepaniak Oscillator

TL;DR

This paper derives the eigenfunctions of the two-dimensional Dirac oscillator, addressing the challenge of bound states in the relativistic regime by adapting Moshinsky's approach.

Contribution

It provides the first explicit eigenfunctions for the 2D Dirac oscillator, extending non-relativistic harmonic oscillator solutions to the relativistic case.

Findings

Eigenfunctions for the 2D Dirac oscillator are explicitly obtained.

The approach adapts Moshinsky's method to relativistic quantum mechanics.

Results contribute to understanding relativistic bound states in two dimensions.

Abstract

While the usual harmonic oscillator potential gives discrete energies in the non-relativistic case, it does not however give genuine bound states in the relativistic case if the potential is treated in the usual way. In the present article, we have obtained the eigenfunctions of the Dirac oscillator in two spatial dimensions, adapting the prescription of Moshinsky.