{
  "annotation_id": "a2658690-de29-4a24-aa5a-5a309624c094",
  "date_created": "2026-03-02T18:01:44.862000Z",
  "date_modified": "2026-03-02T18:01:44.862000Z",
  "file_hash": "d8f28e23a00c98ad1c60f0edac9ba2854cc9ff2b431744d48b6c661d9bf738d1",
  "private": false,
  "record": {
    "abstract": "The amplitude-phase formulation of the Schr\\\"{o}dinger equation is\ninvestigated within the context of uncoupled Ermakov systems, whereby the\namplitude function is given by the auxiliary nonlinear equation. The classical\nlimit of the amplitude and phase functions is analyzed by setting up a\nsemiclassical Ermakov system. In this limit, it is shown that classical\nquantities, such as the classical probability amplitude and the reduced action,\nare obtained only when the semiclassical amplitude and the accumulated phase\nare non-oscillating functions respectively of the space and energy variables.\nConversely, among the infinitely many arbitrary exact quantum amplitude and\nphase functions corresponding to a given wavefunction, only the non-oscillating\nones yield classical quantities in the limit $\\hbar \\to 0$.",
    "arxiv_id": "quant-ph/0106092",
    "authors": [
      "A. Matzkin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/34/38/309",
    "journal_ref": "J. Phys. A : Math. Gen. 34, 7833 (2001).",
    "title": "Non-oscillating solutions to uncoupled Ermakov systems and the   semiclassical limit",
    "url": "https://arxiv.org/abs/quant-ph/0106092"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "52714c06-aa7c-4a58-af55-08b909d9fb87",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}