{
  "annotation_id": "cf5d3fd1-d999-44d6-a470-b49767210c10",
  "date_created": "2026-03-02T18:01:59.657000Z",
  "date_modified": "2026-03-02T18:01:59.657000Z",
  "file_hash": "bad311f70dc66d6057799964ca5311c0af9d93cad1896887ed421d3a9180c29d",
  "private": false,
  "record": {
    "abstract": "Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues.\nThere is numerical evidence that the associated PT-invariant energy eigenstates\nsatisfy an unconventional completeness relation. An ad hoc scalar product among\nthe states is positive definite only if a recently introduced `charge operator\u0027\nis included in its definition. A simple derivation of the conjectured\ncompleteness and orthonormality relations is given. It exploits the fact that\nPT-symmetry provides an additional link between the eigenstates of the\nHamiltonian and those of its adjoint, which form a dual pair of bases. The\n`charge operator\u0027 emerges naturally upon expressing the properties of the dual\nbases in terms of one basis only.",
    "arxiv_id": "quant-ph/0306040",
    "authors": [
      "Stefan Weigert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.68.062111",
    "journal_ref": "Phys. Rev. A 68 (2003) 062111",
    "title": "Completeness and Orthonormality in PT-symmetric Quantum Systems",
    "url": "https://arxiv.org/abs/quant-ph/0306040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1b3739c5-c6f2-4489-b40e-4490af72c1b8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}