Dunkl–Duffin–Kemmer–Petiau equation in (2 + 1) dimensions: The Dunkl–Bosonic oscillator spinless under Landau levels and Coulomb potential

Abstract

In this paper, we consider two fundamental problems in the framework of the Dunkl derivative: the Bosonic oscillator model of spin 0 under magnetic field: Landau levels and the Duffin–Kemmer–Petiau equation with the Coulomb potential. In both cases, we obtain the exact analytical solutions for the bound states in the general case for the different eigenvalues of the reflection operator.

Path integral formulation for Dunkl-Dirac oscillator in (1+1)-dimensional space-time coordinates

“…For example, the one dimensional infinite potential and the harmonic oscillator problem with reflection symmetry is studied in [21], the Dunkl-Coulomb system in the plane is considered in [22], the Dunkl-Coulomb and the Dunkl oscillator models in arbitrary spacedimensions are introduced in [23,24], the Dunkl-Coulomb problem in two dimensions and its coherent states are tested by su(1, 1) algebra in [25], the Dunkl oscillator in the momentum representation and coherent states is presented by Chung et al [26]. The Dunkl-Bosonic oscillator spinless under Landau levels and Coulomb potential are formulated in [27], the exact solution of the relativistic Dunkl oscillator in two and three dimensions, respectively considered in [28,29], the Landau levels for the (2+ 1) Dunkl-Klein-Gordon oscillator is presented in [30], in [31] the generalized Dunkl oscillator is studied in the Cartesian system and finally in [32] analyzed the generalized Fokker-Planck equation in terms of Dunkl-type derivatives.…”

The Klein-Gordon and Dirac oscillators with generalized Dunkl derivative

“…For the extension to the relativistic case, we find the one-dimensional Dunkl-Dirac oscillator treated in [21,22], the 2 dimensions case for Dunkl-Dirac oscillator coupled to an external magnetic field is exposed in [23], the Dunkl-Coulomb potential and the Landau levels for the 2 dimensions Dunkl-Klein-Gordon oscillator by [24,25] the Dunkl-Klein-Gordon oscillator and Coulomb potential in 3 dimensions in [26], Dunkl graphene in constant magnetic field in [27] and the Dunkl-Duffin-Kemmer-Petiau oscillator under Landau levels and Coulomb potential in [28,29]. On the other hand, the generalization of this Dunkl theory is incorporated, certain forms with different parameters have been presented and some physical problems are treated [30,31].…”