Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space

TL;DR

This paper provides an exact solution for the two-dimensional Dunkl harmonic oscillator in non-commutative phase space, revealing new parity-related features and demonstrating the advantages of using Dunkl operators over traditional derivatives.

Contribution

It introduces an exact analytical solution for the Dunkl harmonic oscillator in non-commutative phase space, highlighting the richer structure and parity distinctions.

Findings

Eigenvalues derived in terms of Laguerre functions

Dunkl-Harmonic Oscillator differs from the ordinary case in parity properties

Dunkl operator offers more detailed information

Abstract

In this paper, we examine the harmonic oscillator problem in non-commutative phase space (NCPS) by using the Dunkl derivative instead of the habitual one. After defining the Hamilton operator, we use the polar coordinates to derive the binding energy eigenvalue. We find eigenfunctions that correspond to these eigenvalues in terms of the Laguerre functions. We observe that the Dunkl-Harmonic Oscillator (DHO) in the NCPS differs from the ordinary one in the context of providing additional information on the even and odd parities. Therefore, we conclude that working with the Dunkl operator could be more appropriate because of its rich content.