{
  "annotation_id": "188c4bce-4d4f-4602-8112-ae2110b03e7a",
  "date_created": "2026-03-02T18:02:48.304000Z",
  "date_modified": "2026-03-02T18:02:48.304000Z",
  "file_hash": "3289b4575a84a765f756632840083b78933f216b36701493ab8c96d5b444105e",
  "private": false,
  "record": {
    "abstract": "By a series of simple examples, we illustrate how the lack of mathematical\nconcern can readily lead to surprising mathematical contradictions in wave\nmechanics. The basic mathematical notions allowing for a precise formulation of\nthe theory are then summarized and it is shown how they lead to an elucidation\nand deeper understanding of the aforementioned problems. After stressing the\nequivalence between wave mechanics and the other formulations of quantum\nmechanics, i.e. matrix mechanics and Dirac\u0027s abstract Hilbert space\nformulation, we devote the second part of our paper to the latter approach: we\ndiscuss the problems and shortcomings of this formalism as well as those of the\nbra and ket notation introduced by Dirac in this context. In conclusion, we\nindicate how all of these problems can be solved or at least avoided.",
    "arxiv_id": "quant-ph/9907069",
    "authors": [
      "F. Gieres"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th",
      "math-ph",
      "math.MP",
      "nucl-th",
      "physics.ed-ph"
    ],
    "doi": "10.1088/0034-4885/63/12/201",
    "journal_ref": "Rep.Prog.Phys. 63 (2000) 1893",
    "title": "Mathematical surprises and Dirac\u0027s formalism in quantum mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9907069"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ee5af01b-7210-42bd-a169-17f60416bc96",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}