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

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 to zero, our results are adequately reduced to those reported in the literature.