{
  "annotation_id": "492f980b-f95e-4543-90c8-af2485265e73",
  "date_created": "2026-03-02T18:01:38.682000Z",
  "date_modified": "2026-03-02T18:01:38.682000Z",
  "file_hash": "adecf8f7557e66ee5564e836bbb7e04e04025445dc91c41bd9511aa89f4e9cb3",
  "private": false,
  "record": {
    "abstract": "The Dirac equation for an electron in two spatial dimensions in the Coulomb\nand homogeneous magnetic fields is discussed. For weak magnetic fields, the\napproximate energy values are obtained by semiclassical method. In the case\nwith strong magnetic fields, we present the exact recursion relations that\ndetermine the coefficients of the series expansion of wave functions, the\npossible energies and the magnetic fields. It is found that analytic solutions\nare possible for a denumerably infinite set of magnetic field strengths. This\nsystem thus furnishes an example of the so-called quasi-exactly solvable\nmodels. A distinctive feature in the Dirac case is that, depending on the\nstrength of the Coulomb field, not all total angular momentum quantum number\nallow exact solutions with wavefunctions in reasonable polynomial forms.\nSolutions in the nonrelativistic limit with both attractive and repulsive\nCoulomb fields are briefly discussed by means of the method of factorization.",
    "arxiv_id": "quant-ph/0003086",
    "authors": [
      "Choon-Lin Ho",
      "V. R. Khalilov"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevA.61.032104",
    "journal_ref": "Phys.Rev. A61 (2000) 032104",
    "title": "Planar Dirac Electron in Coulomb and Magnetic Fields",
    "url": "https://arxiv.org/abs/quant-ph/0003086"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a4cc7c35-b2d9-47bb-a870-ab825fe75209",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}