{
  "annotation_id": "0cf38d86-d824-40e7-85ab-559cff2e2b09",
  "date_created": "2026-03-02T18:01:45.466000Z",
  "date_modified": "2026-03-02T18:01:45.466000Z",
  "file_hash": "71b8dff60613f5de0efef3a33f12a3dbcdf326badce4355133d2413cf0054f5f",
  "private": false,
  "record": {
    "abstract": "The Schroedinger operator with point interaction in one dimension has a U(2)\nfamily of self-adjoint extensions. We study the spectrum of the operator and\nshow that (i) the spectrum is uniquely determined by the eigenvalues of the\nmatrix U belonging to U(2) that characterizes the extension, and that (ii) the\nspace of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius\nstrip with boundary. We employ a parametrization of U(2) that admits a direct\nphysical interpretation and furnishes a coherent framework to realize the\nspectral duality and anholonomy recently found. This allows us to find that\n(iii) physically distinct point interactions form a three-parameter quotient\nspace of the U(2) family.",
    "arxiv_id": "quant-ph/0105066",
    "authors": [
      "Izumi Tsutsui",
      "Tamas Fulop",
      "Taksu Cheon"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1415432",
    "journal_ref": "Journal of Mathematical Physics 42 (2001) 5687-5697",
    "title": "Moebius Structure of the Spectral Space of Schroedinger Operators with   Point Interaction",
    "url": "https://arxiv.org/abs/quant-ph/0105066"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a19ce719-0aa2-41ed-b10e-77ff8012a44e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}