{
  "annotation_id": "6d7aa86c-abe6-473f-ac88-f784c4b40d70",
  "date_created": "2026-03-02T18:02:44.191000Z",
  "date_modified": "2026-03-02T18:02:44.191000Z",
  "file_hash": "7084c26d73db74fa2b4d43d92dde18d62682ecf34077ecdd204356b8a0782864",
  "private": false,
  "record": {
    "abstract": "We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger\nHamiltonian H = -\\Delta + vf(x) in one dimension is known for all values of the\ncoupling v \u003e 0. The potential shape f(x) is assumed to be symmetric, bounded\nbelow, and monotone increasing for x \u003e 0. A fast algorithm is devised which\nallows the potential shape f(x) to be reconstructed from the energy trajectory\nF(v). Three examples are discussed in detail: a shifted power-potential, the\nexponential potential, and the sech-squared potential are each reconstructed\nfrom their known exact energy trajectories.",
    "arxiv_id": "quant-ph/9812058",
    "authors": [
      "Richard L. Hall"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.532712",
    "journal_ref": "J.Math.Phys. 40 (1999) 699-707",
    "title": "Constructive inversion of energy trajectories in quantum mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9812058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "598afbd9-3aa7-406c-8544-f2a9a449791a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}