Exact solutions of the (2+1) -dimensional Dirac oscillator under a magnetic field in the presence of a minimal length in the noncommutative phase-space

TL;DR

This paper derives exact solutions for a (2+1)-dimensional Dirac oscillator under a magnetic field within a noncommutative phase space incorporating minimal length, revealing how noncommutativity influences relativistic quantum systems.

Contribution

It provides the first exact solutions of the Dirac oscillator in noncommutative phase space with minimal length, connecting the problem to a Poschl-Teller potential.

Findings

Eigenvalues are explicitly calculated.

Wave functions are expressed in hypergeometric functions.

The noncommutative framework modifies the energy spectrum.

Abstract

We consider a two-dimensional Dirac oscillator in the presence of magnetic field in noncommutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl-Teller potential. The eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.