{
  "annotation_id": "a0f26bb5-3ae1-4a8f-a57a-99f06b59c6f4",
  "date_created": "2026-03-02T18:02:15.961000Z",
  "date_modified": "2026-03-02T18:02:15.961000Z",
  "file_hash": "c16df3c83f251ecc7d1f1b33cb7b0504c0c761c21422da0a0350b13960a39400",
  "private": false,
  "record": {
    "abstract": "In this paper, the quantum spectrum of isochronous potentials is\ninvestigated. Given that the frequency of the classical motion in such\npotentials is energy-independent, it is natural to expect their quantum spectra\nto be equispaced. However, as it has already been shown in some specific\nexamples, this property is not always true. To gain some general insight into\nthis problem, a WKB analysis of the spectrum, valid for any analytic potential,\nis performed and the first semiclassical corrections to its regular spacing are\ncalculated. We illustrate the results on the two-parameter family of\nisochronous potentials derived in [1], which includes the harmonic oscillator,\nthe asymmetric parabolic well, the radial harmonic oscillator and Urabe\u0027s\npotential as special limiting cases. In addition, some new analytical\nexpressions for families of isochronous potentials and their corresponding\nspectra are derived by means of the above-mentioned method.",
    "arxiv_id": "quant-ph/0504074",
    "authors": [
      "J. Dorignac"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/27/007",
    "title": "On the quantum spectrum of isochronous potentials",
    "url": "https://arxiv.org/abs/quant-ph/0504074"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d7ea1650-0113-4e9a-8897-0a06ab74bdb3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}