{
  "annotation_id": "b2b12fce-e4ca-4d8d-b6df-e2752a4bc7ec",
  "date_created": "2026-03-02T18:02:47.576000Z",
  "date_modified": "2026-03-02T18:02:47.576000Z",
  "file_hash": "278e3ac1c4b7696c57d297d90177ce3cb9dcc4187edf428433bbf45ec4640d44",
  "private": false,
  "record": {
    "abstract": "Version 1: The well known Eckart\u0027s singular s-wave potential is\nPT-symmetrically regularized and continued to the whole real line. The new\nmodel remains exactly solvable and its bound states remain proportional to\nJacobi polynomials. Its real and discrete spectrum exhibits several unusual\nfeatures.\n  Version 2: Parity times time-reversal symmetry of complex Hamiltonians with\nreal spectra is usually interpreted as a weaker mathematical substitute for\nHermiticity. Perhaps an equally important role is played by the related\nstrengthened analyticity assumptions. In a constructive illustration we\ncomplexify a few potentials solvable only in s-wave. Then we continue their\ndomain from semi-axis to the whole axis and get the new exactly solvable\nmodels. Their energies come out real as expected. The new one-dimensional\nspectra themselves differ quite significantly from their s-wave predecessors.",
    "arxiv_id": "quant-ph/9912027",
    "authors": [
      "Miloslav Znojil"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/33/24/311",
    "journal_ref": "J. Phys. A: Math. Gen. 33 (2000) 4561 - 4572",
    "title": "PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials",
    "url": "https://arxiv.org/abs/quant-ph/9912027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "de370e28-8156-4cb3-887a-31a226478437",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}