{
  "annotation_id": "c5b99b99-94f2-4e12-9a6c-879558e88642",
  "date_created": "2026-03-02T18:02:00.291000Z",
  "date_modified": "2026-03-02T18:02:00.291000Z",
  "file_hash": "22634b785f745887bd72102d42fcf33283fb1ee3c0fb713c97af0ce989eb934b",
  "private": false,
  "record": {
    "abstract": "We define pseudo-reality and pseudo-adjointness of a Hamiltonian, $H$, as\n$\\rho H \\rho^{-1}=H^\\ast$ and $\\mu H \\mu^{-1}=H^\\prime$, respectively. We prove\nthat the former yields the {\\it necessary} condition for spectrum to be real\nwhereas the latter helps in fixing a definition for inner-product of the\neigenstates. Here we separate out adjointness of an operator from its\nHermitian-adjointness. It turns out that a Hamiltonian possessing real spectrum\nis first pseudo-real, further it could be Hermitian, PT-symmetric or\npseudo-Hermitian.",
    "arxiv_id": "quant-ph/0306093",
    "authors": [
      "Zafar Ahmed"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/41/005",
    "title": "Pseudo-reality and pseudo-adjointness of Hamiltonians",
    "url": "https://arxiv.org/abs/quant-ph/0306093"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3f6a6f5b-2747-4543-9496-cf5dd3f7ac43",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}