{
  "annotation_id": "042a5b1c-3764-4e0d-8db2-a14f9a544bf2",
  "date_created": "2026-03-02T18:02:23.622000Z",
  "date_modified": "2026-03-02T18:02:23.622000Z",
  "file_hash": "7cae2b20f2979de78da6e76924bcd34354eb97fc53d78268479d71c4ff2c07e0",
  "private": false,
  "record": {
    "abstract": "There exists a Klein-Gordon-like equation for a spin-1/2 particle in an\nelectromagnetic field with 2-spinors as wave functions that is a direct\nconsequence of the corresponding Dirac equation. Thus, it reproduces the same\nbinding energies for an electron in a hydrogen atom as the Dirac equation.\nThere is also a square-root equation for 2-spinors which can give the same\nbinding energies up to the forth order of the fine structure constant,\ninclusively, what will be shown by means of a comparison of the\nnon-relativistic limit plus a first relativistic correction of both equations\nfor 2-spinors within the framework of a perturbation analysis. A parallel will\nalso be drawn to the spin-0 case.",
    "arxiv_id": "quant-ph/0602047",
    "authors": [
      "Tobias Gleim"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Klein-Gordon and square-root operator equations for two-spinors and   scalars: perturbation calculations for hydrogen-like systems",
    "url": "https://arxiv.org/abs/quant-ph/0602047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "506f144e-dd7e-40ab-8ddf-15ecb838d7e6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}