{
  "annotation_id": "d78049f2-7a9f-4b8b-bbfc-4c2ee86a0f80",
  "date_created": "2026-03-02T18:02:12.706000Z",
  "date_modified": "2026-03-02T18:02:12.706000Z",
  "file_hash": "bdc85e3e25118dfd3557b3235410ffd0582e4af76f862bbbf6c78e5bd005ca5b",
  "private": false,
  "record": {
    "abstract": "An algebraic non-perturbative approach is proposed for the analytical\ntreatment of Schr\\\"{o}dinger equations with a potential that can be expressed\nin terms of an exactly solvable piece with an additional potential. Avoiding\ndisadvantages of standard approaches, new handy recursion formulae with the\nsame simple form both for ground and excited states have been obtained. As an\nillustration the procedure, well adapted to the use of computer algebra, is\nsuccessfully applied to quartic anharmonic oscillators by means of very simple\nalgebraic manipulations. The trend of the exact values of the energies is\nrather well reproduced for a large range of values of the coupling constant\n(g=0.001-10000).",
    "arxiv_id": "quant-ph/0412162",
    "authors": [
      "B. Gonul",
      "N. Celik",
      "E. Olgar"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217732305016737",
    "journal_ref": "Mod. Phys. Lett. A 20 (2005) 1683",
    "title": "A New Algebraic Approach to Perturbation Theory",
    "url": "https://arxiv.org/abs/quant-ph/0412162"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f673a960-fba8-42e9-990d-a88df234b383",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}