{
  "annotation_id": "b0583659-5f49-4d3a-8fac-3b7693526bed",
  "date_created": "2026-03-02T18:02:34.710000Z",
  "date_modified": "2026-03-02T18:02:34.710000Z",
  "file_hash": "345275593656dadf0288f9bdec3fce22ddb5c578e89331a7729d0797877ba715",
  "private": false,
  "record": {
    "abstract": "The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector\nelectromagnetic fields is considered. Using two over-simplified examples (the\nDirac-Coulomb and Dirac-oscillator fields), we report energy-levels crossing as\na spectral property or as an effect of the hidden supersymmetric quantum\nmechanical language and/or quasi-parity signatures. Under different settings of\nthe related interactions\u0027 way-of-coupling into Dirac equation, it is observed\nthat the two ultimate/effective descendents, Dirac-Coulomb and\nDirac-oscillator, exhibit different conditions on the energy-levels crossings.",
    "arxiv_id": "quant-ph/0703078",
    "authors": [
      "Omar Mustafa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-007-9564-2",
    "journal_ref": "Int. J. Theor. Phys. 47, 1300 (2008)",
    "title": "Energy-levels crossing and radial Dirac equation: Supersymmetry and   quasi-parity spectral signatures",
    "url": "https://arxiv.org/abs/quant-ph/0703078"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e758c3db-2cde-47a6-8c34-a33f47892060",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}