{
  "annotation_id": "6bd2eb57-f4b0-4276-87d9-1362c8160b18",
  "date_created": "2026-03-02T18:01:56.613000Z",
  "date_modified": "2026-03-02T18:01:56.613000Z",
  "file_hash": "ba1586a641954abc2b097485668d2a60d811dc319ef7e4951ae188bff643b6a9",
  "private": false,
  "record": {
    "abstract": "The system whose Hamiltonian is a linear combination of the generators of\nSU(1,1) group with time-dependent coefficients is studied. It is shown that\nthere is a unitary relation between the system and a system whose Hamiltonian\nis simply proportional to the generator of the compact subgroup of the SU(1,1).\nThe unitary relation is described by the classical solutions of a\ntime-dependent (harmonic) oscillator. Making use of the relation, the wave\nfunctions satisfying the Schr\\\"{o}dinger equation are given for a general\nunitary representation in terms of the matrix elements of a finite group\ntransformation (Bargmann function). The wave functions of the harmonic\noscillator with an inverse-square potential is studied in detail, and it is\nshown that, through an integral, the model provides a way of deriving the\nBargmann function for the representation of positive discrete series of the\nSU(1,1).",
    "arxiv_id": "quant-ph/0303143",
    "authors": [
      "Dae-Yup Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.68.012108",
    "journal_ref": "Phys. Rev. A 68, 012108 (2003)",
    "title": "Unitary relation for the time-dependent SU(1,1) systems",
    "url": "https://arxiv.org/abs/quant-ph/0303143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55950f68-4672-4a9a-82cf-43f042d3e942",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}