Energy Spectrum of a 2D Dirac Oscillator in the Presence of the Aharonov-Bohm Effect

TL;DR

This paper analyzes the energy spectrum of a 2D Dirac oscillator influenced by the Aharonov-Bohm effect, revealing dependence on particle spin and magnetic flux, with special energy values for irregular solutions and a nonrelativistic limit.

Contribution

It provides a detailed calculation of the energy spectrum considering the AB effect, including irregular solutions and the nonrelativistic limit, which advances understanding of relativistic quantum systems with magnetic flux.

Findings

Energy spectrum depends on particle spin and magnetic flux

Irregular solutions lead to specific energy values

Nonrelativistic limit aligns with classical results

Abstract

We determine the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator in the presence of Aharonov-Bohm (AB) effect . It is shown that the energy spectrum depends on the spin of particle and the AB magnetic flux parameter. Finally, when the irregular solution occurs it is shown that the energy takes particular values. The nonrelativistic limit is also considered.