Dunkl–Klein–Gordon Equation in Three-Dimensions: The Klein–Gordon Oscillator and Coulomb Potential

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Hamil B., LÜTFÜOĞLU B. C.

Few-Body Systems, vol.63, no.4, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1007/s00601-022-01776-8
  • Journal Name: Few-Body Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.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.