Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator

TL;DR

This paper derives the Landau levels for a Dunkl-Klein-Gordon oscillator in 2+1 dimensions under a magnetic field, using algebraic and analytical methods, and confirms consistency with known results.

Contribution

It introduces a novel algebraic approach to find the energy spectrum of the Dunkl-Klein-Gordon oscillator coupled to a magnetic field.

Findings

Derived the Landau levels algebraically using $su(1,1)$ Lie algebra.

Obtained analytical solutions for energy spectrum and eigenfunctions.

Results reduce to known cases when magnetic field or Dunkl parameters are zero.

Abstract

In this paper we study the $(2+1)$-dimensional Klein-Gordon oscillator coupled to an external magnetic field, in which we change the standard partial derivatives for the Dunkl derivatives. We find the energy spectrum (Landau levels) in an algebraic way, by introducing three operators that close the $su(1,1)$ Lie algebra and from the theory of unitary representations. Also we find the energy spectrum and the eigenfunctions analytically, and we show that both solutions are consistent. Finally, we demonstrate that when the magnetic field vanishes or when the parameters of the Dunkl derivatives are set zero, our results are adequately reduced to those reported in the literature.