{
  "annotation_id": "12841f12-2f09-4650-afe7-320a0e0e1e5f",
  "date_created": "2026-03-02T18:02:41.424000Z",
  "date_modified": "2026-03-02T18:02:41.424000Z",
  "file_hash": "8b5b66ec401d3b2da8c0d39cd4d3f7cb8e385eb938976927bcedd9193b51c510",
  "private": false,
  "record": {
    "abstract": "Quantum mechanical models and practical calculations often rely on some\nexactly solvable models like the Coulomb and the harmonic oscillator\npotentials. The $D$ dimensional generalized Coulomb potential contains these\npotentials as limiting cases, thus it establishes a continuous link between the\nCoulomb and harmonic oscillator potentials in various dimensions. We present\nresults which are necessary for the utilization of this potential as a model\nand practical reference problem for quantum mechanical calculations. We define\na Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate\nthe Green\u0027s operator on this basis and also present an SU(1,1) algebra\nassociated with it. We formulate the problem for the one-dimensional case too,\nand point out that the complications arising due to the singularity of the\none-dimensional Coulomb problem can be avoided with the use of the generalized\nCoulomb potential.",
    "arxiv_id": "quant-ph/9802012",
    "authors": [
      "G. L\u00e9vai",
      "B. K\u00f3nya",
      "Z. Papp"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532595",
    "journal_ref": "J.Math.Phys. 39 (1998) 5811-5823",
    "title": "Unified treatment of the Coulomb and harmonic oscillator potentials in   $D$ dimensions",
    "url": "https://arxiv.org/abs/quant-ph/9802012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "10c022fa-4959-432f-aec0-5e550d2cb32a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}