{
  "annotation_id": "763d1d3d-1b15-4602-adba-9a076eb91565",
  "date_created": "2026-03-02T18:02:37.837000Z",
  "date_modified": "2026-03-02T18:02:37.837000Z",
  "file_hash": "834f3c1bbf73eaa045f32e5af0d2bebf9cb88d2681365343b853b5345581e913",
  "private": false,
  "record": {
    "abstract": "Quantum canonical transformations corresponding to the action of the unitary\noperator $e^{i\\epsilon(t)\\sqrt{f(x)}p\\sqrt{f(x)}}$ is studied. It is shown that\nfor $f(x)=x$, the effect of this transformation is to rescale the position and\nmomentum operators by $e^{\\epsilon(t)}$ and $e^{-\\epsilon(t)}$, respectively.\nThis transformation is shown to lead to the identification of a previously\nunknown class of exactly solvable time-dependent harmonic oscillators. It turns\nout that the Caldirola-Kanai oscillator whose mass is given by $m=m_0 e^{\\gamma\nt}$, belongs to this class. It is also shown that for arbitrary $f(x)$, this\ncanonical transformations map the dynamics of a free particle with constant\nmass to that of free particle with a position-dependent mass. In other words,\nthey lead to a change of the metric of the space.",
    "arxiv_id": "quant-ph/9612038",
    "authors": [
      "Ali Mostafazadeh"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "title": "On a Class of Quantum Canonical Transformations and the Time-Dependent   Harmonic Oscillator",
    "url": "https://arxiv.org/abs/quant-ph/9612038"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "482a96b8-d8ac-464b-a364-a96c8dd05327",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}