{
  "annotation_id": "1d39c438-f2a9-4c07-8c90-ceb17b4b117a",
  "date_created": "2026-03-02T18:02:03.311000Z",
  "date_modified": "2026-03-02T18:02:03.311000Z",
  "file_hash": "77da1dae0c8057156211f199c4f9450a234f0f868b8089931883acd2ea172939",
  "private": false,
  "record": {
    "abstract": "Historically the starting point of wave mechanics is the Planck and\nEinstein-de Broglie relations for the energy and momentum of a particle, where\nthe momentum is connected to the group velocity of the wave packet. We\ntranslate the arguments given by de Broglie to the case of a wave defined on\nthe grid points of a space-time lattice and explore the physical consequences\nsuch as integral period, wave length, discrete energy, momentum and rest mass.",
    "arxiv_id": "quant-ph/0401011",
    "authors": [
      "M. Lorente"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Einstein-De Broglie relations on the lattice",
    "url": "https://arxiv.org/abs/quant-ph/0401011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a2bb169d-41e7-4cc4-ac9a-e837d05cda4e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}