{
  "annotation_id": "ac2b2db6-01eb-42f8-a4c5-815a358cb475",
  "date_created": "2026-03-02T18:02:47.316000Z",
  "date_modified": "2026-03-02T18:02:47.316000Z",
  "file_hash": "7df7bc15fb6df75440d01b8728df7fd47b506e19efdfed8c7fddb17962ace13a",
  "private": false,
  "record": {
    "abstract": "A systematic semiclassical expansion of the hydrogen problem about the\nclassical Kepler problem is shown to yield remarkably accurate results. Ad hoc\nchanges of the centrifugal term, such as the standard Langer modification where\nthe factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical\nenergy levels are shown to be exact to first order in $\\hbar$ with all higher\norder contributions vanishing. The wave functions and dipole matrix elements\nare also discussed.",
    "arxiv_id": "quant-ph/9904103",
    "authors": [
      "Joachim Hainz",
      "Hermann Grabert"
    ],
    "categories": [
      "quant-ph",
      "physics.atom-ph"
    ],
    "doi": "10.1103/PhysRevA.60.1698",
    "title": "Centrifugal terms in the WKB approximation and semiclassical   quantization of hydrogen",
    "url": "https://arxiv.org/abs/quant-ph/9904103"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "262cdf49-515f-43ca-a4eb-de7081f61a8e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}