{
  "annotation_id": "8a04ed18-d1de-4538-b759-963f5a7699f2",
  "date_created": "2026-03-02T18:02:44.851000Z",
  "date_modified": "2026-03-02T18:02:44.851000Z",
  "file_hash": "196c7d21de10cebcbb87981bc6aa3380c8ef757c5cbc35840ae998aaf99c8e17",
  "private": false,
  "record": {
    "abstract": "The explicit semiclassical treatment of logarithmic perturbation theory for\nthe nonrelativistic bound states problem is developed. Based upon\n$\\hbar$-expansions and suitable quantization conditions a new procedure for\nderiving perturbation expansions for the one-dimensional anharmonic oscillator\nis offered. Avoiding disadvantages of the standard approach, new handy\nrecursion formulae with the same simple form both for ground and exited states\nhave been obtained. As an example, the perturbation expansions for the energy\neigenvalues of the harmonic oscillator perturbed by $\\lambda x^{6}$ are\nconsidered.",
    "arxiv_id": "quant-ph/9902086",
    "authors": [
      "I. V. Dobrovolska",
      "R. S. Tutik"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/32/3/011",
    "journal_ref": "J.Phys.A32:563-568,1999",
    "title": "Semiclassical treatment of logarithmic perturbation theory",
    "url": "https://arxiv.org/abs/quant-ph/9902086"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a5c60305-6572-435c-9187-48dfe6caa38f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}