{
  "annotation_id": "a4e127dd-7d23-4847-9353-d91358de4140",
  "date_created": "2026-03-02T18:00:46.955000Z",
  "date_modified": "2026-03-02T18:00:46.955000Z",
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  "record": {
    "abstract": "The paraxial approximation to the scalar Helmholtz equation is shown to be\nequivalent to the Schr\\\"odinger equation for a quantum harmonic oscillator.\nThis equivalence maps the Gouy-phase of classical wave optics onto the time\ncoordinate of the quantum harmonic oscillator and also helps us understand the\nqualitative behavior of the field and intensity distributions of focused\noptical beams in terms of the amplitude and probability distributions of\nquantum harmonic oscillators and vice versa.",
    "arxiv_id": "physics/0312116",
    "authors": [
      "Ole Steuernagel"
    ],
    "categories": [
      "physics.optics",
      "physics.gen-ph"
    ],
    "doi": "10.1119/1.1900099",
    "journal_ref": "Am. J. Phys. 73, 625 (2005)",
    "title": "Equivalence between focussed paraxial beams and the quantum harmonic   oscillator",
    "url": "https://arxiv.org/abs/physics/0312116"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a7392d01-f03f-458f-a671-46e4d35ad820",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}