{
  "annotation_id": "d74f43cc-3618-41d6-ad19-1414d7388ece",
  "date_created": "2026-03-02T18:01:49.443000Z",
  "date_modified": "2026-03-02T18:01:49.443000Z",
  "file_hash": "72298c715210891f5e23b630eb055084ea4506f17909d7af67f6bfe507635405",
  "private": false,
  "record": {
    "abstract": "For quantum mechanics on a lattice the position (``particle number\u0027\u0027)\noperator and the quasi-momentum (``phase\u0027\u0027) operator obey canonical commutation\nrelations (CCR) only on a dense set of the Hilbert space. We compare exact\nnumerical results for a particle in simple potentials on the lattice with the\nexpectations, when the CCR are assumed to be strictly obeyed. Only for\nsufficiently smooth eigenfunctions this leads to reasonable results. In the\nlong time limit the use of the CCR can lead to a qualitativel wrong dynamics\neven if the initial state is in the dense set.",
    "arxiv_id": "quant-ph/0204139",
    "authors": [
      "K. Schonhammer"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el"
    ],
    "doi": "10.1103/PhysRevA.66.014101",
    "title": "Canonically conjugate pairs and phase operators",
    "url": "https://arxiv.org/abs/quant-ph/0204139"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8e5967b9-3864-435c-9919-ab0aa25c7cf0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}