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

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.