Effect of the Wigner-Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

Abstract

In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner-Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue equation and the corresponding wave function for Dirac harmonic oscillator and Dirac equation, respectively. It is shown all results in the limit state satisfied what we had expected before.