Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential

Abstract

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate solutions for two important problems in three-dimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the Dunkl-Klein-Gordon oscillator solutions with the Cartesian and spherical coordinates. In both coordinate systems, we find that the differential equations are separable and their eigenfunctions can be given in terms of the associate Laguerre and Jacobi polynomials. We observe how the Dunkl formalism is affecting the eigenvalues as well as the eigenfunctions. As a second problem, we examine the Dunkl-Klein-Gordon equation with the Coulomb potential. We obtain the eigenvalue, their corresponding eigenfunctions, and the Dunkl-fine structure terms.

Thermal Properties of Relativistic Dunkl Oscillators

“…A Dunkl operator, D, can be defined as a linear superposition of differential and difference operators [5] for use in various problems in mathematics [6][7][8] and theoretical physics [9][10][11][12][13][14]. Especially in recent years, we observe that this interest has increased in the context of relativistic and non-relativistic quantum mechanical problems [15][16][17][18][19][20][21][22][23][24][25][26].…”

“…Since the Dunkl operator carries a parity operator, it can allow obtaining additional information in the classical solutions. According to this motivation, some authors already examined Dunkl-Dirac [15,17], Dunkl-Klein-Gordon [23,26], Dunkl-pseudo harmonic [24] and Dunkl-Duffin-Kemmer-Petiau [25] oscillators under various scenario and dimensions.…”