{
  "annotation_id": "f974e97c-e571-4b72-aa96-9ee73e33901c",
  "date_created": "2026-03-02T18:02:44.977000Z",
  "date_modified": "2026-03-02T18:02:44.977000Z",
  "file_hash": "67647374c38e7fa550d9782b9b0067f0fe5cc666c310abea9d328c161c729bfa",
  "private": false,
  "record": {
    "abstract": "One-dimensional scattering problems are of wide physical interest and are\nencountered in many diverse applications. In this article I establish some very\ngeneral bounds for reflection and transmission coefficients for one-dimensional\npotential scattering. Equivalently, these results may be phrased as general\nbounds on the Bogolubov coefficients, or statements about the transfer matrix.\nA similar analysis can be provided for the parametric change of frequency of a\nharmonic oscillator. A number of specific examples are discussed---in\nparticular I provide a general proof that sharp step function potentials always\nscatter more effectively than the corresponding smoothed potentials. The\nanalysis also serves to collect together and unify what would otherwise appear\nto be quite unrelated results.",
    "arxiv_id": "quant-ph/9901030",
    "authors": [
      "Matt Visser"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevA.59.427",
    "journal_ref": "Phys.Rev. A59 (1999) 427-438",
    "title": "Some general bounds for 1-D scattering",
    "url": "https://arxiv.org/abs/quant-ph/9901030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9e3def2c-3b3c-4793-ab19-d91175668a01",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}