{
  "annotation_id": "8f274fdb-67c7-46f6-9c3a-25d0a64333e2",
  "date_created": "2026-03-02T18:02:27.218000Z",
  "date_modified": "2026-03-02T18:02:27.218000Z",
  "file_hash": "f1f50ceded8bb6f60e7cb99b13883cf34333b41c95888809066e8e29e71a6935",
  "private": false,
  "record": {
    "abstract": "Excited bound states are often understood within scattering based theories as\nresulting from the collision of a particle on a target via a short-range\npotential. We show that the resulting formalism is non-Hermitian and describe\nthe Hilbert spaces and metric operator relevant to a correct formulation of\nsuch theories. The structure and tools employed are the same that have been\nintroduced in current works dealing with PT-symmetric and quasi-Hermitian\nproblems. The relevance of the non-Hermitian formulation to practical\ncomputations is assessed by introducing a non-Hermiticity index. We give a\nnumerical example involving scattering by a short-range potential in a Coulomb\nfield for which it is seen that even for a small but non-negligible\nnon-Hermiticity index the non-Hermitian character of the problem must be taken\ninto account. The computation of physical quantities in the relevant Hilbert\nspaces is also discussed.",
    "arxiv_id": "quant-ph/0603238",
    "authors": [
      "A. Matzkin"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1088/0305-4470/39/34/017",
    "journal_ref": "J. Phys. A: Math. Gen. 39, 10859, 2006",
    "title": "Non-Hermitian quantum mechanics: the case of bound state scattering   theory",
    "url": "https://arxiv.org/abs/quant-ph/0603238"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0ae1c088-21a1-487a-9cad-8096bd5dd9b5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}