{
  "annotation_id": "fe09d364-edc6-499f-b3ef-6e7c105fa1ca",
  "date_created": "2026-03-02T18:02:48.581000Z",
  "date_modified": "2026-03-02T18:02:48.581000Z",
  "file_hash": "9c1fec50ca4dea68fda0cf28df4adf4e547469173ee4bb10a8dc11b7a093f3e5",
  "private": false,
  "record": {
    "abstract": "Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H\n= -Delta + vf(x), where the potential shape f(x) is symmetric and monotone\nincreasing for x \u003e 0, and the coupling parameter v is positive.\n  If the \u0027kinetic potential\u0027 bar{f}(s) associated with f(x) is defined by the\ntransformation: bar{f}(s) = F\u0027(v), s = F(v)-vF\u0027(v),then f can be reconstructed\nfrom F by the sequence: f^{[n+1]} = bar{f} o bar{f}^{[n]^{-1}} o f^{[n]}.\nConvergence is proved for special classes of potential shape; for other test\ncases it is demonstrated numerically. The seed potential shape f^{[0]} need not\nbe \u0027close\u0027 to the limit f.",
    "arxiv_id": "quant-ph/9912032",
    "authors": [
      "Richard L. Hall"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0375-9601(99)00872-5",
    "journal_ref": "Phys. Lett. A265, 28-34 (2000)",
    "title": "Functional inversion for potentials in quantum mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9912032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e822fe12-326d-44d9-bfa5-7c47ebdce383",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}