Generalized Dirac Oscillators with position-dependent mass

TL;DR

This paper investigates a generalized Dirac oscillator with a position-dependent mass in one dimension, analyzing bound states under various conditions including electric fields, and identifying critical electric field values for bound state existence.

Contribution

It introduces a novel analysis of the Dirac oscillator with position-dependent mass, including bound state solutions and electric field effects, expanding understanding of relativistic quantum systems.

Findings

Bound states with zero and non-zero energy are obtained.

Existence of bound states depends on the electric field magnitude.

Critical electric field value determines bound state viability.

Abstract

We study the $(1+1)$ dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non zero energy have been obtained for suitable choices of the mass function/oscillator interaction. It has also been shown that in the presence of an electric field, bound states exist if the magnitude of the electric field does not exceed a critical value.