Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

TL;DR

This paper studies the three-dimensional Dirac oscillator within a deformed Snyder-de Sitter algebra, deriving its energy spectrum and wavefunctions using supersymmetric quantum mechanics and shape invariance.

Contribution

It introduces a novel analysis of the Dirac oscillator in Snyder-de Sitter space, revealing effects of minimal uncertainties on its quantum properties.

Findings

Derived energy spectrum and wavefunctions for the Dirac oscillator in Snyder-de Sitter space.

Showed the impact of minimal position and momentum uncertainties on the oscillator.

Applied supersymmetric quantum mechanics and shape invariance techniques successfully.

Abstract

Three dimensional Dirac oscillator was considered in deformed space obeyed to deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations gives rise to appearance minimal uncertainty in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator supersymmetric quantum mechanics and shape invariance technique was applied.