{
  "annotation_id": "9834889b-b7bd-4c47-abcf-eec9ce66d68e",
  "date_created": "2026-03-02T18:01:46.071000Z",
  "date_modified": "2026-03-02T18:01:46.071000Z",
  "file_hash": "5c3cf67d481d8934cff6ceaa205a419ce01ca3282da3a9b923159f5c963a7cc5",
  "private": false,
  "record": {
    "abstract": "In formal scattering theory, Green functions are obtained as solutions of a\ndistributional equation. In this paper, we use the Sturm-Liouville theory to\ncompute Green functions within a rigorous mathematical theory. We shall show\nthat both the Sturm-Liouville theory and the formal treatment yield the same\nGreen functions. We shall also show how the analyticity of the Green functions\nas functions of the energy keeps track of the so-called ``incoming\u0027\u0027 and\n``outgoing\u0027\u0027 boundary conditions.",
    "arxiv_id": "quant-ph/0107096",
    "authors": [
      "R. de la Madrid"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1016/S0960-0779(01)00083-2",
    "journal_ref": "Chaos, Solitons \u0026 Fractals 12 (2001) 2689-2695",
    "title": "Formal and Precise Derivation of the Green Functions for a Simple   Potential",
    "url": "https://arxiv.org/abs/quant-ph/0107096"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "09155b54-6dc3-4fc1-a45f-6e793f630d87",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}