{
  "id": "quant-ph/0502105",
  "version": "v1",
  "published": "2005-02-17T12:55:25.000Z",
  "updated": "2005-02-17T12:55:25.000Z",
  "title": "Kepler problem in Dirac theory for a particle with position-dependent mass",
  "authors": [
    "I. O. Vakarchuk"
  ],
  "comment": "9 pages",
  "doi": "10.1088/0305-4470/38/21/016",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the expression for the mass is smaller than the classical electron radius $e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$ even in the absence of the Coulomb interaction. Quasirelativistic expansion of the energy has been carried out, and a modified expression for the fine structure of energy levels has been obtained. The problem of kinetic energy operator in the Schr\\\"odinger equation is discussed for the case of position-dependent mass. In particular, we have found that for highly excited states the mutual ordering of the inverse mass and momentum operator in the non-relativistic theory is not important.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-17T12:55:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "position-dependent mass",
      "kepler problem",
      "dirac theory",
      "bound states",
      "kinetic energy operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}