{
  "annotation_id": "f1179916-97eb-4ad7-b282-c66bb5928a4b",
  "date_created": "2026-03-02T18:01:38.496000Z",
  "date_modified": "2026-03-02T18:01:38.496000Z",
  "file_hash": "dfba92cfc543c121f842327f8764d50b1d61a190928b3983605000a77f95a0fd",
  "private": false,
  "record": {
    "abstract": "Recurrence formulae for arbitrary hydrogenic radial matrix elements are\nobtained in the Dirac form of relativistic quantum mechanics. Our approach is\ninspired on the relativistic extension of the second hypervirial method that\nhas been succesfully employed to deduce an analogous relationship in non\nrelativistic quantum mechanics. We obtain first the relativistic extension of\nthe second hypervirial and then the relativistic recurrence relation.\nFurthermore, we use such relation to deduce relativistic versions of the\nPasternack-Sternheimer rule and of the virial theorem.",
    "arxiv_id": "quant-ph/0004099",
    "authors": [
      "R P Mart\u00ednez-y-Romero",
      "H N N\u00fa\u00f1ez-Y\u00e9pez",
      "A L Salas-Brito"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "physics.atom-ph"
    ],
    "doi": "10.1088/0953-4075/33/10/101",
    "title": "Recurrence relation for relativistic atomic matrix elements",
    "url": "https://arxiv.org/abs/quant-ph/0004099"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8f9a48a3-c420-4fd9-b588-399052a612a4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}