{
  "annotation_id": "37536eca-cdc3-49ec-86e4-dddf1c07bbad",
  "date_created": "2026-03-02T18:01:56.628000Z",
  "date_modified": "2026-03-02T18:01:56.628000Z",
  "file_hash": "ec33a8bb8d01ef6ccc3627cd33359d6914729d6e11e81a50a9c8031725b3f59e",
  "private": false,
  "record": {
    "abstract": "The explicit semiclassical treatment of logarithmic perturbation theory for\nthe bound-state problem within the framework of the radial Klein-Gordon\nequation with attractive real-analytic screened Coulomb potentials, contained\ntime-component of a Lorentz four-vector and a Lorentz-scalar term, is\ndeveloped. Based upon $\\hbar$-expansions and suitable quantization conditions a\nnew procedure for deriving perturbation expansions is offered. Avoiding\ndisadvantages of the standard approach, new handy recursion formulae with the\nsame simple form both for ground and excited states have been obtained. As an\nexample, the perturbation expansions for the energy eigenvalues for the\nHulth\\\u0027en potential containing the vector part as well as the scalar component\nare considered.",
    "arxiv_id": "quant-ph/0212087",
    "authors": [
      "I. V. Dobrovolska",
      "R. S. Tutik"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217751X0401955X",
    "journal_ref": "International Journal of Modern Physics A, Vol. 19, No. 22 (2004)\n  3669-3683",
    "title": "Logarithmic perturbation theory for radial Klein-Gordon equation with   screened Coulomb potentials via $\\hbar$ expansions",
    "url": "https://arxiv.org/abs/quant-ph/0212087"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e3041e30-95ae-4cf9-bdc9-9ccd5631b545",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}