{
  "id": "quant-ph/0503166",
  "version": "v1",
  "published": "2005-03-19T16:43:11.000Z",
  "updated": "2005-03-19T16:43:11.000Z",
  "title": "On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions",
  "authors": [
    "I. O. Vakarchuk"
  ],
  "comment": "13 pages",
  "doi": "10.1088/0305-4470/38/34/010",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The Dirac equation has been studied in which the Dirac matrices $\\hat{\\boldmath$\\alpha$}, \\hat\\beta$ have space factors, respectively $f$ and $f_1$, dependent on the particle's space coordinates. The $f$ function deforms Heisenberg algebra for the coordinates and momenta operators, the function $f_1$ being treated as a dependence of the particle mass on its position. The properties of these functions in the transition to the Schr\\\"odinger equation are discussed. The exact solution of the Dirac equation for the particle motion in the Coulomnb field with a linear dependence of the $f$ function on the distance $r$ to the force centre and the inverse dependence on $r$ for the $f_1$ function has been found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-19T16:43:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformed heisenberg algebra",
      "exact solution",
      "dirac theory",
      "dirac equation",
      "function deforms heisenberg algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1370571
    }
  }
}