{
  "annotation_id": "9bbd2dbc-e21d-40fb-94b7-60ccced10c00",
  "date_created": "2026-03-02T18:02:27.106000Z",
  "date_modified": "2026-03-02T18:02:27.106000Z",
  "file_hash": "58bd99b2013cde4cfb70531bd4e65fa88f5083360b8ca4ce18491b4fcff338c0",
  "private": false,
  "record": {
    "abstract": "The annihilation-creation operators of the harmonic oscillator, the basic and\nmost important tools in quantum physics, are generalised to most solvable\nquantum mechanical systems of single degree of freedom including the so-called\n`discrete\u0027 quantum mechanics. They admit exact Heisenberg operator solution. We\npresent unified definition of the annihilation-creation operators (a^{(\\pm)})\nas the positive/negative frequency parts of the exact Heisenberg operator\nsolution.",
    "arxiv_id": "quant-ph/0605221",
    "authors": [
      "Satoru Odake",
      "Ryu Sasaki"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.CA",
      "math.MP",
      "nlin.SI"
    ],
    "doi": "10.1016/j.physletb.2006.08.017",
    "journal_ref": "Phys.Lett. B641 (2006) 112-117",
    "title": "Exact solution in the Heisenberg picture and annihilation-creation   operators",
    "url": "https://arxiv.org/abs/quant-ph/0605221"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8cd62ddd-7997-4d03-9e8d-7b434b5aafa7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}