{
  "annotation_id": "c82bb793-adfb-46d3-abeb-d96578f42b59",
  "date_created": "2026-03-02T18:02:13.074000Z",
  "date_modified": "2026-03-02T18:02:13.074000Z",
  "file_hash": "b7021e6a1a4bbed1f28698835248c5ca529ff60fd7e8804717925f76ed395c0a",
  "private": false,
  "record": {
    "abstract": "Exact solution of Dirac equation for a particle whose potential energy and\nmass are inversely proportional to the distance from the force centre has been\nfound. The bound states exist provided the length scale $a$ which appears in\nthe expression for the mass is smaller than the classical electron radius\n$e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$\neven in the absence of the Coulomb interaction. Quasirelativistic expansion of\nthe energy has been carried out, and a modified expression for the fine\nstructure of energy levels has been obtained. The problem of kinetic energy\noperator in the Schr\\\"odinger equation is discussed for the case of\nposition-dependent mass. In particular, we have found that for highly excited\nstates the mutual ordering of the inverse mass and momentum operator in the\nnon-relativistic theory is not important.",
    "arxiv_id": "quant-ph/0502105",
    "authors": [
      "I. O. Vakarchuk"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/21/016",
    "title": "Kepler problem in Dirac theory for a particle with position-dependent   mass",
    "url": "https://arxiv.org/abs/quant-ph/0502105"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a15862f4-1a38-4f1a-bde6-52bae0fa9e30",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}