DunklKleinGordon Equation in ThreeDimensions: The KleinGordon 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 operatorbased deformation and we investigate solutions for two important problems in threedimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the DunklKleinGordon 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 DunklKleinGordon equation with the Coulomb potential. We obtain the eigenvalue, their corresponding eigenfunctions, and the Dunklfine structure terms.
 Publication:

FewBody Systems
 Pub Date:
 December 2022
 DOI:
 10.1007/s00601022017768
 arXiv:
 arXiv:2112.09948
 Bibcode:
 2022FBS....63...74H
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 8 pages, 1 fig