{
  "annotation_id": "68446aa2-bac0-493f-b6a5-69fc1af3b4ad",
  "date_created": "2026-03-02T18:02:03.183000Z",
  "date_modified": "2026-03-02T18:02:03.183000Z",
  "file_hash": "f1c3b3eb31a260929730eec5bac1addcf30a98b81cfce7fe46e530472ecc0315",
  "private": false,
  "record": {
    "abstract": "The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy\nunconventional completeness and orthonormality relations. These relations\nreflect the properties of a pair of bi-orthonormal bases associated with\nnon-hermitean diagonalizable operators. In a similar vein, such a dual pair of\nbases is shown to possess, in the presence of PT symmetry, a Gram matrix of a\nparticular structure: its inverse is obtained by simply swapping the signs of\nsome its matrix elements.",
    "arxiv_id": "quant-ph/0310050",
    "authors": [
      "Stefan Weigert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1023/B:CJOP.0000014380.30604.a8",
    "journal_ref": "Czech. J. Phys. 54 (2004) 147",
    "title": "The Gram Matrix of a PT-symmetric Quantum System",
    "url": "https://arxiv.org/abs/quant-ph/0310050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9758b7f7-325c-4f5a-9704-272ccebddc8c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}