{
  "annotation_id": "0990b33f-207e-4494-a3e4-5e698adf7e83",
  "date_created": "2026-03-02T18:01:18.200000Z",
  "date_modified": "2026-03-02T18:01:18.200000Z",
  "file_hash": "330d71bcf21e74bccb1a66bcc8246e5bbeb400b91c00cc64bcd1957c116dff71",
  "private": false,
  "record": {
    "abstract": "The boundary integral method for calculating the stationary states of a\nquantum particle in nano-devices and quantum billiards is presented in detail\nat an elementary level. According to the method, wave functions inside the\ndomain of the device or billiard are expressed in terms of line integrals of\nthe wave function and its normal derivative along the domain\u0027s boundary; the\nrespective energy eigenvalues are obtained as the roots of Fredholm\ndeterminants. Numerical implementations of the method are described and applied\nto determine the energy level statistics of billiards with circular and stadium\nshapes and demonstrate the quantum mechanical characteristics of chaotic\nmotion. The treatment of other examples as well as the advantages and\nlimitations of the boundary integral method are discussed.",
    "arxiv_id": "physics/9702022",
    "authors": [
      "Ioan Kosztin",
      "Klaus Schulten"
    ],
    "categories": [
      "physics.comp-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/S0129183197000278",
    "journal_ref": "Int.J.Mod.Phys. C8 (1997) 293-325",
    "title": "Boundary Integral Method for Stationary States of Two-Dimensional   Quantum Systems",
    "url": "https://arxiv.org/abs/physics/9702022"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f2b519d6-ebae-44b8-bffa-d129c1f0ed01",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}