{
  "annotation_id": "836e85e0-3e6b-4d89-a69b-fadf189ffcea",
  "date_created": "2026-03-02T18:02:38.117000Z",
  "date_modified": "2026-03-02T18:02:38.117000Z",
  "file_hash": "73aed267423fb5ff9c50416f1582919ef603eb6cb6b1bb7fe940a249041a1160",
  "private": false,
  "record": {
    "abstract": "We perform a systematic WKB expansion to all orders for a one-dimensional\nsystem with potential $V(x)=U_0/\\cos^2{(\\alpha x)}$. We are able to sum the\nseries to the exact energy spectrum. Then we show that at any finite order the\nerror of the WKB approximation measured in the natural units of the mean energy\nlevel spacing does not go to zero when the quantum number goes to infinity.\nTherefore we make the general conclusion that the semiclassical approximations\nfail to predict the individual energy levels within a vanishing fraction of the\nmean energy level spacing.",
    "arxiv_id": "quant-ph/9610027",
    "authors": [
      "Marko Robnik",
      "Luca Salasnich"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "nucl-th"
    ],
    "doi": "10.1088/0305-4470/30/5/031",
    "journal_ref": "J.Phys.A30:1711-1718,1997",
    "title": "WKB to all orders and the accuracy of the semiclassical quantization",
    "url": "https://arxiv.org/abs/quant-ph/9610027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dcbbef30-a4bb-41d1-a6e1-f22e2f637218",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}