{
  "annotation_id": "86bbe758-565a-41bf-872a-9aa748355378",
  "date_created": "2026-03-02T18:01:56.465000Z",
  "date_modified": "2026-03-02T18:01:56.465000Z",
  "file_hash": "8642b4ada64f26014e4035c16823032590c7f77f8527051188ebf2459952b7a4",
  "private": false,
  "record": {
    "abstract": "The known approaches of number-phase problem (for a quantum oscillator) are\nmutually contradictory. All of them are subsequent in respect with the\nRobertson-Schr\\\"{o}dinger uncertainty relation (RSUR). In oposition here it is\nproposed a new approacch aimed to be aboriginal as regard RSRUR. From the new\nperspective the Dirac\u0027s operators for vibrational number and phase appear as\ncorrect mathematical tools while the alluded problem receives a natural\nsolution. PACS codes: 03.65.-w, 03.65.Ca, 03.65.Fd, 03.65.Ta Keywords: quantum\noscillator, number and phase, uncertainty relations.",
    "arxiv_id": "quant-ph/0211143",
    "authors": [
      "S. Dumitru"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the number-phase problem",
    "url": "https://arxiv.org/abs/quant-ph/0211143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a3d4c2a3-45fb-4a68-88e9-685af12f24e8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}