{
  "annotation_id": "4fff5d93-6c3a-461f-935d-9adad9b26907",
  "date_created": "2026-03-02T18:01:56.567000Z",
  "date_modified": "2026-03-02T18:01:56.567000Z",
  "file_hash": "daba219dc8fe86f55b4c0b642a4168fc07026616345ad882577ee5fb913d8cd3",
  "private": false,
  "record": {
    "abstract": "In a recent paper it was shown that if a Hamiltonian H has an unbroken PT\nsymmetry, then it also possesses a hidden symmetry represented by the linear\noperator C. The operator C commutes with both H and PT. The inner product with\nrespect to CPT is associated with a positive norm and the quantum theory built\non the associated Hilbert space is unitary. In this paper it is shown how to\nconstruct the operator C for the non-Hermitian PT-symmetric Hamiltonian\n$H={1\\over2}p^2+{1\\over2}x^2 +i\\epsilon x^3$ using perturbative techniques. It\nis also shown how to construct the operator C for\n$H={1\\over2}p^2+{1\\over2}x^2-\\epsilon x^4$ using nonperturbative methods.",
    "arxiv_id": "quant-ph/0211166",
    "authors": [
      "Carl M. Bender",
      "Peter N. Meisinger",
      "Qinghai Wang"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/7/312",
    "title": "Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum   Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0211166"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "093c9483-4f34-4677-b288-a8679cfdf4de",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}