{
  "annotation_id": "97baf04e-b152-4023-91cc-ac3c67d19911",
  "date_created": "2026-03-02T18:01:53.002000Z",
  "date_modified": "2026-03-02T18:01:53.002000Z",
  "file_hash": "58308a8bfb16385edb35c086e427594ddee8c9e471f50df35db7a08064650e70",
  "private": false,
  "record": {
    "abstract": "The Fourier transform is often used to connect the Lorentzian energy\ndistribution for resonance scattering to the exponential time dependence for\ndecaying states. However, to apply the Fourier transform, one has to bend the\nrules of standard quantum mechanics; the Lorentzian energy distribution must be\nextended to the full real axis $-\\infty\u003cE\u003c\\infty$ instead of being bounded from\nbelow $0\\leq E \u003c\\infty$ (``Fermi\u0027s approximation\u0027\u0027). Then the Fourier transform\nof the extended Lorentzian becomes the exponential, but only for times $t\\geq\n0$, a time asymmetry which is in conflict with the unitary group time evolution\nof standard quantum mechanics. Extending the Fourier transform from\ndistributions to generalized vectors, we are led to Gamow kets, which possess a\nLorentzian energy distribution with $-\\infty\u003cE\u003c\\infty$ and have exponential\ntime evolution for $t\\geq t_0 =0$ only. This leads to probability predictions\nthat do not violate causality.",
    "arxiv_id": "quant-ph/0206145",
    "authors": [
      "A. Bohm",
      "N. L. Harshman",
      "H. Walther"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.012107",
    "journal_ref": "Phys. Rev. A 66 (2002), 012107 1-11",
    "title": "Relating the Lorentzian and exponential: Fermi\u0027s approximation,the   Fourier transform and causality",
    "url": "https://arxiv.org/abs/quant-ph/0206145"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "08ed826e-f7a1-42c1-a94c-b3e57b6969e5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}