{
  "annotation_id": "f9535067-da48-40db-98ba-eacc91874607",
  "date_created": "2026-03-02T18:01:37.956000Z",
  "date_modified": "2026-03-02T18:01:37.956000Z",
  "file_hash": "0bc571f8c79f30573f6c6f5fad678b3aa1e99c7679f0e8565e0927bb291e0c33",
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  "record": {
    "abstract": "The unitary operator which transforms a harmonic oscillator system of\ntime-dependent frequency into that of a simple harmonic oscillator of different\ntime-scale is found, with and without an inverse-square potential. It is shown\nthat for both cases, this operator can be used in finding complete sets of wave\nfunctions of a generalized harmonic oscillator system from the well-known sets\nof the simple harmonic oscillator. Exact invariants of the time-dependent\nsystems can also be obtained from the constant Hamiltonians of unit mass and\nfrequency by making use of this unitary transformation. The geometric phases\nfor the wave functions of a generalized harmonic oscillator with an\ninverse-square potential are given.",
    "arxiv_id": "quant-ph/0002065",
    "authors": [
      "Dae-Yup Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.62.014103",
    "journal_ref": "Physical Review A 62 (2000) 014103",
    "title": "Unitary relation between a harmonic oscillator of time-dependent   frequency and a simple harmonic oscillator with and without an inverse-square   potential",
    "url": "https://arxiv.org/abs/quant-ph/0002065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d930db36-79ee-4031-a524-99f83cf86860",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}