Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators

TL;DR

This paper explores relativistic solutions for generalized Dunkl harmonic and anharmonic oscillators in two dimensions, revealing how Wigner parameters influence degeneracy, using Nikiforov-Uvarov and QES methods.

Contribution

It introduces the use of a three-parameter generalized Dunkl derivative in relativistic oscillator equations, expanding the analytical framework for these quantum systems.

Findings

Degenerate states depend on Wigner parameter values.

Solutions obtained via Nikiforov-Uvarov and QES methods.

Enhanced understanding of parity and reflection effects in relativistic oscillators.

Abstract

Dunkl derivative enriches solutions by discussing parity due to its reflection operator. Very recently, one of the authors of this manuscript presented one of the most general forms of Dunkl derivative that depends on three Wigner parameters to have a better tuning. In this manuscript, we employ the latter generalized Dunkl derivative in a relativistic equation to examine two-dimensional harmonic and anharmonic oscillators solutions. We obtain the solutions by Nikiforov-Uvarov and QES methods, respectively. We show that degenerate states can occur according to the Wigner parameter values.