{
  "annotation_id": "a0d988e4-1d3f-4ea6-b2b4-2f344bdd3912",
  "date_created": "2026-03-02T18:02:27.039000Z",
  "date_modified": "2026-03-02T18:02:27.039000Z",
  "file_hash": "91505718d87fb7def2e2283971227a214f7e7bc06f8071cb5926854c82deabc8",
  "private": false,
  "record": {
    "abstract": "We analyze dynamical consequences of a conjecture that there exists a\nfundamental (indivisible) quant of time. In particular we study the problem of\ndiscrete energy levels of hydrogen atom. We are able to reconstruct potential\nwhich in discrete time formalism leads to energy levels of unperturbed hydrogen\natom. We also consider linear energy levels of quantum harmonic oscillator and\nshow how they are produced in the discrete time formalism. More generally, we\nshow that in discrete time formalism finite motion in central potential leads\nto discrete energy spectrum, the property which is common for quantum\nmechanical theory. Thus deterministic (but discrete time!) dynamics is\ncompatible with discrete energy levels.",
    "arxiv_id": "quant-ph/0604199",
    "authors": [
      "Andrei Khrennikov",
      "Yaroslav Volovich"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.2158749",
    "title": "Energy Levels of \"Hydrogen Atom\" in Discrete Time Dynamics",
    "url": "https://arxiv.org/abs/quant-ph/0604199"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e2aa81af-8845-40d6-a982-7fc4745a3142",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}