The 2D $\kappa$-Dirac oscillator

TL;DR

This paper investigates the 2D Dirac oscillator within a quantum deformed framework based on the $$-Poincaré-Hopf algebra, showing that deformation alters energy levels and wave functions.

Contribution

It introduces a $$-deformed Dirac equation for the 2D oscillator, revealing how quantum deformation impacts its energy spectrum and wave functions.

Findings

Deformation modifies the energy spectrum of the 2D Dirac oscillator.

Wave functions are affected by the $$-deformation parameter.

Theoretical formulation within the $$-Poincaré-Hopf algebra framework.

Abstract

In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra is considered. The problem is formulated using the $\kappa$-deformed Dirac equation. The resulting theory reveals that the energies and wave functions of the oscillator are modified by the deformation parameter.