{
  "annotation_id": "eb17023d-9626-47ce-86b4-c038a20133b8",
  "date_created": "2026-03-02T18:00:42.342000Z",
  "date_modified": "2026-03-02T18:00:42.342000Z",
  "file_hash": "78d3013ef167c029428c79081703d5a5fd7a27980eeb106d04548a1862e50fae",
  "private": false,
  "record": {
    "abstract": "The exact Green function for the scalar wave equation in a plane with any set\nof perfectly reflecting straight mirrors, which may be joined to form corners,\nis given as a diffraction scattering series. Instances would be slit\ndiffraction in optics, or the Schrodinger equation inside (or outside) a\ngeneral polygonal enclosure (\u0027quantum polygon billiards\u0027). The method is based\non the seminal 1896 Riemann helicoid surface solution by Sommerfeld for optical\ndiffraction by a single corner. It is generalised to account for multiple\nscatter by adapting the analysis of Stovicek for a closely related problem: a\ncollection of magnetic flux lines (points) in a plane, the multi-flux\nAharonov-Bohm effect. The short wavelength limit is shown to yield the\n\u0027geometrical theory of diffraction\u0027. For slit diffraction the exact series is\nshown to coincide with that of Schwarzschild in 1902.",
    "arxiv_id": "physics/0303093",
    "authors": [
      "J. H. Hannay",
      "A. Thain"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.1088/0305-4470/36/14/310",
    "title": "Exact scattering theory for any straight reflectors in two dimensions",
    "url": "https://arxiv.org/abs/physics/0303093"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d0b8ca0f-c0b6-4fec-8686-f6f7b104b02d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}