{
  "annotation_id": "d9d976fa-8dee-43cd-bb24-e3b257884f8c",
  "date_created": "2026-03-02T18:02:37.941000Z",
  "date_modified": "2026-03-02T18:02:37.941000Z",
  "file_hash": "c237e6d8fe64bed9c732e51a02b369a7d0a9ebfd0a86e7f7874639e0d4abb5a3",
  "private": false,
  "record": {
    "abstract": "We formulate scattering in one dimension due to the coupled Schr\\\"{o}dinger\nequation in terms of the $S$ matrix, the unitarity of which leads to\nconstraints on the scattering amplitudes. Levinson\u0027s theorem is seen to have\nthe form $\\eta(0) = \\pi (n_b + 1/2 n - 1/2 N)$, where $\\eta(0)$ is the phase of\nthe $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero\nbinding energy, $n$ the number of half-bound states, and $N$ the number of\ncoupled equations. In view of the effects due to the half-bound states, the\nthreshold behaviour of the scattering amplitudes is investigated in general,\nand is also illustrated by means of particular potential models.",
    "arxiv_id": "quant-ph/9608032",
    "authors": [
      "K. A. Kiers",
      "W. van Dijk"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.531762",
    "journal_ref": "J.Math.Phys.37:6033-6059,1996",
    "title": "Scattering in one dimension: The coupled Schroedinger equation,   threshold behaviour and Levinson\u0027s theorem",
    "url": "https://arxiv.org/abs/quant-ph/9608032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "708dd083-4e48-4b0e-870d-21f05056853b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}