Relativistic solutions of generalized-Dunkl harmonic and anharmonic 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 quasi-exact solvability (QES) methods, respectively. We show that degenerate states can occur according to the Wigner parameter values.