{
  "annotation_id": "c4c3bfc0-197e-4bb0-ad91-247e553916c3",
  "date_created": "2026-03-02T18:02:45.248000Z",
  "date_modified": "2026-03-02T18:02:45.248000Z",
  "file_hash": "7162ae987c8ad610dd297329486040847dbb32de15f32f8940805fe78764881c",
  "private": false,
  "record": {
    "abstract": "Quantum canonical transformations corresponding to time-dependent\ndiffeomorphisms of the configuration space are studied. A special class of\nthese transformations which correspond to time-dependent dilatations is used to\nidentify a previously unknown class of exactly solvable time-dependent harmonic\noscillators. The Caldirola-Kanai oscillator belongs to this class. For a\ngeneral time-dependent harmonic oscillator, it is shown that choosing the\ndilatation parameter to satisfy the classical equation of motion, one obtains\nthe solution of the Schr\\\"odinger equation. A simple generalization of this\nresult leads to the reduction of the Schr\\\"odinger equation to a second order\nordinary differential equation whose special case is the auxiliary equation of\nthe Lewis-Riesenfeld invariant theory. Time-evolution operator is expressed in\nterms of a positive real solution of this equation in a closed form, and the\ntime-dependent position and momentum operators are calculated.",
    "arxiv_id": "quant-ph/9807002",
    "authors": [
      "Ali Mostafazadeh"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th"
    ],
    "doi": "10.1088/0305-4470/31/30/014",
    "journal_ref": "J.Phys.A31:6495-6503,1998",
    "title": "Time-Dependent Diffeomorphisms as Quantum Canonical Transformations and   the Time-Dependent Harmonic Oscillator",
    "url": "https://arxiv.org/abs/quant-ph/9807002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea48a5b0-4706-4ef2-864a-fa465f170920",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}