{
  "id": "2008.13204",
  "version": "v1",
  "published": "2020-08-30T15:53:57.000Z",
  "updated": "2020-08-30T15:53:57.000Z",
  "title": "Exact Solutions of the $2D$ Dunkl-Klein-Gordon Equation: The Coulomb Potential and the Klein-Gordon Oscillator",
  "authors": [
    "R. D. Mota",
    "D. Ojeda-Guillén",
    "M. Salazar-Ramírez",
    "V. D. Granados"
  ],
  "comment": "15 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In this paper, we begin from the Klein-Gordon ($KG$) equation in $2D$ and change the standard partial derivatives by the Dunkl derivatives to obtain the Dunkl-Klein-Gordon ($DKG$) equation. We show that the generalization with Dunkl derivative of the $z$-component of the angular momentum is what allows the separation of variables of the $DKG$ equation. Then, we show that $DKG$ equations for the $2D$ Coulomb potential and the Klein-Gordon oscillator are exactly solvable. For each of the problems, we find the energy spectrum from an algebraic point of view by introducing suitable sets of operators which close the $su(1,1)$ algebra and use the unitary theory of representations. Also, we find analytically the energy spectrum and eigenfunctions of the $DKG$ equations for both problems. Finally, we show that when the parameters of the Dunkl derivative vanish, our results are suitably reduced to those reported in the literature for these $2D$ problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T15:53:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "klein-gordon oscillator",
      "coulomb potential",
      "exact solutions",
      "dunkl-klein-gordon equation",
      "energy spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}