{
  "annotation_id": "9fdd41bd-479c-4c5b-96e8-ff2e1339da7d",
  "date_created": "2026-03-02T18:01:56Z",
  "date_modified": "2026-03-02T18:01:56Z",
  "file_hash": "36d0e5cfe1282cb7725fd1aff2860df6ce9fc47315b141fbe392aa234d78298b",
  "private": false,
  "record": {
    "abstract": "The propagator associated to the potential barrier $V=V_{0}\\cosh ^{-2}(\\omega\nx)$ is obtained by solving path integrals. The method of delta functionals\nbased on canonical and other transformations is used to reduce the path\nintegral for this potential into a path integral for the Morse potential\nproblem. The dimensional extension technique is seen to be essential for\nperforming the multiple integral representation of the propagator. The\ncorrectly normalized scattering wave functions and the scattering function are\nderived. To test the method employed, the free particle and the $\\delta\n-$function barrier are considered as limiting cases.",
    "arxiv_id": "quant-ph/0302009",
    "authors": [
      "L. Guechi",
      "T. F. Hammann"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Il Nuovo Cimento 115 B (2000) 123",
    "title": "On the path integration for the potential barrier $V_{0}\\cosh   ^{-2}(\\omega x)$",
    "url": "https://arxiv.org/abs/quant-ph/0302009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "58e66c36-bf0a-4e37-87c0-a13fa33585f5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}