{
  "annotation_id": "d53251db-ed37-461e-8d32-e12eb508d38e",
  "date_created": "2026-03-02T18:02:34.050000Z",
  "date_modified": "2026-03-02T18:02:34.050000Z",
  "file_hash": "dda12bd8ffe708afaa6434b9cdacd03047851836a1383679481cbaafa9e126d5",
  "private": false,
  "record": {
    "abstract": "The frequency of a classical periodic system and the energy levels of the\ncorresponding quantum system can both be obtained using action variables. We\ndemonstrate the construction of two forms of the action variable for a one\ndimensional harmonic oscillator in classical, relativistic and quantum regimes.\nThe relativistic effects are considered as perturbative, within the context of\na non-relativistic quantum formalism. The transition of the relativistic\nquantum system to both classical relativistic and classical non-relativistic\nregimes is illustrated in a unified framework. Formulas for the frequency of a\nclassical relativistic oscillator and the energy eigenvalues of the\ncorresponding quantum oscillator for the weak relativistic case are derived.\nAlso studied are the non-relativistic and classical limits of these formulas\nwhich provide valuable insights on the parallels between relativistic and\nnon-relativistic systems on the one hand and between classical and quantum\nsystems on the other.",
    "arxiv_id": "quant-ph/0702106",
    "authors": [
      "M. K. Balasubramanya"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Frequencies and energy levels of the weakly relativistic harmonic   oscillator from the action variable",
    "url": "https://arxiv.org/abs/quant-ph/0702106"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4bfc5d30-7859-459c-9d03-d68ceb4daebc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}