{
  "annotation_id": "6883c131-9649-4a43-98bc-740bbe576199",
  "date_created": "2026-03-02T18:02:48.418000Z",
  "date_modified": "2026-03-02T18:02:48.418000Z",
  "file_hash": "c23a43823c7b450004e0a08b5c60c2482428824d481df59cf9052cf7c9050575",
  "private": false,
  "record": {
    "abstract": "The scattering of Dirac particles by symmetric potentials in one dimension is\nstudied. A Levinson theorem is established. By this theorem, the number of\nbound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase\nshifts $\\eta_+(\\pm E_k)$ [$\\eta_-(\\pm E_k)$] of scattering states with the same\nparity at zero momentum as follows: $$\\eta_\\pm(\\mu)+\\eta_\\pm(-\\mu)\\pm{\\pi\\over\n2}[\\sin^2\\eta_\\pm(\\mu) -\\sin^2\\eta_\\pm(-\\mu)]=n_\\pm\\pi.$$ The theorem is\nverified by several simple examples.",
    "arxiv_id": "quant-ph/9912078",
    "authors": [
      "Qiong-gui Lin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s100530050379",
    "journal_ref": "Eur. Phys. J. D 7 (1999) 515-524",
    "title": "Levinson theorem for Dirac particles in one dimension",
    "url": "https://arxiv.org/abs/quant-ph/9912078"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3a090b73-b862-4c10-8c3d-8c7671faed00",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}