{
  "annotation_id": "2be1925c-9234-418c-87cf-1a3c313f288f",
  "date_created": "2026-03-02T18:01:56.621000Z",
  "date_modified": "2026-03-02T18:01:56.621000Z",
  "file_hash": "4253cea7cf52d78ac38e59ce2a9eced2b6569c786b6f8009e72772d6d3c6dd3a",
  "private": false,
  "record": {
    "abstract": "The so$(2,1)$ Lie algebra is applied to three classes of two- and\nthree-dimensional Smorodinsky-Winternitz super-integrable potentials for which\nthe path integral discussion has been recently presented in the literature. We\nhave constructed the Green\u0027s functions for two important super-integrable\npotentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we\nhave considered two examples, one is maximally super-integrable and another one\nminimally super-integrable. The discussion is made in various coordinate\nsystems. The energy spectrum and the suitably normalized wave functions of\nbound and continuous states are then deduced.",
    "arxiv_id": "quant-ph/0302130",
    "authors": [
      "L. Chetouani",
      "L. Guechi",
      "T. F. Hammann"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "J. Math. Phys. 42 (2001) 4684 - 4707",
    "title": "Algebraic treatment of super-integrable potentials",
    "url": "https://arxiv.org/abs/quant-ph/0302130"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "10ed6039-48b0-40dc-bfd8-d24395628f09",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}