Remarks on the Dirac oscillator in $(2+1)$ dimensions

TL;DR

This paper analyzes the Dirac oscillator in (2+1) dimensions, solving it in polar coordinates, revealing degeneracy conditions, and identifying an isolated bound state solution beyond previous studies.

Contribution

It provides a comprehensive solution in polar coordinates and clarifies degeneracy conditions, including the existence of an isolated bound state not previously reported.

Findings

Degeneracy of energy spectrum can occur for all values of $sm$

Existence of an isolated bound state solution beyond Sturm-Liouville analysis

Dependence of energy levels on spin parameter and angular momentum

Abstract

In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of $sm$. In an additional analysis, we also show that an isolated bound state solution, excluded from Sturm-Liouville problem, exists.