{
  "annotation_id": "8ffaf095-ec85-47ec-9124-17d9b6874fb6",
  "date_created": "2026-03-02T18:01:38.562000Z",
  "date_modified": "2026-03-02T18:01:38.562000Z",
  "file_hash": "7b6bfc59766cb07360fd6a6a078cbdd48c3ffcd3d590b4b4129214ae610cd328",
  "private": false,
  "record": {
    "abstract": "The time operator, an operator which satisfies the canonical commutation\nrelation with the Hamiltonian, is investigated, on the basis of a certain\nalgebraic relation for a pair of operators T and H, where T is symmetric and H\nself-adjoint. This relation is equivalent to the Weyl relation, in the case of\nself-adjoint T, and is satisfied by the Aharonov-Bohm time operator T_0 and the\nfree Hamiltonian H_0 for the one-dimensional free-particle system. In order to\nsee the qualitative properties of T_0, the operators T and H satisfying this\nalgebraic relation are examined. In particular, it is shown that the standard\ndeviation of T is directly connected to the survival probability, and H is\nabsolutely continuous. Hence, it is concluded that the existence of the\noperator T implies the existence of scattering states. It is also shown that\nthe minimum uncertainty states do not exist. Other examples of these operators\nT and H, than the one-dimensional free-particle system, are demonstrated.",
    "arxiv_id": "quant-ph/0006085",
    "authors": [
      "Manabu Miyamoto"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1346598",
    "title": "A generalized Weyl relation approach to the time operator and its   connection to the survival probability",
    "url": "https://arxiv.org/abs/quant-ph/0006085"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fd17e3c7-2f6d-45c8-b6ff-8ceb164854a7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}