{
  "annotation_id": "5596c938-0be7-4615-aeb0-58e77b69c909",
  "date_created": "2026-03-02T18:02:41.535000Z",
  "date_modified": "2026-03-02T18:02:41.535000Z",
  "file_hash": "72bb55e1925fb3fc1794106cdcaa34e3f859cd9af6c420c168b0b3cc46aa0c71",
  "private": false,
  "record": {
    "abstract": "The Schr\\\"odinger equation is thoroughly analysed for the isotropic\noscillator in the three-dimensional space of constant positive curvature in the\nspherical and cylindrical systems of coordinates. The expansion coefficients\nbetween the spherical and cylindrical bases of the oscillator are calculated.\nIt is shown that the relevant coefficients are expressed through the\ngeneralised hypergeometric functions $_4F_3$ of the unit argument or $6_j$\nRacah symbols extended over their indices to the region of real values.\nLimiting transitions to a free motion and flat space are considered in detail.\nElliptic bases of the oscillator are constructed in the form of expansion over\nthe spherical and cylindrical bases. The corresponding expansion coefficients\nare shown to obey the three-term recurrence relations.",
    "arxiv_id": "quant-ph/9710045",
    "authors": [
      "Ye. M. Hakobyan",
      "G. S. Pogosyan",
      "A. N. Sissakian",
      "S. I. Vinitsky"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "journal_ref": "Phys. Atom. Nucl. 62 (1999) 623-637; Yad. Fiz . 62 (1999) 671-685",
    "title": "Isotropic oscillator in the space of constant positive curvature.   Interbasis expansions",
    "url": "https://arxiv.org/abs/quant-ph/9710045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8d76861c-57ea-402b-8ec7-5774907094a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}