{
  "id": "quant-ph/9912032",
  "version": "v1",
  "published": "1999-12-07T17:34:59.000Z",
  "updated": "1999-12-07T17:34:59.000Z",
  "title": "Functional inversion for potentials in quantum mechanics",
  "authors": [
    "Richard L. Hall"
  ],
  "comment": "14 pages, 2 figures",
  "journal": "Phys. Lett. A265, 28-34 (2000)",
  "doi": "10.1016/S0375-9601(99)00872-5",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H = -Delta + vf(x), where the potential shape f(x) is symmetric and monotone increasing for x > 0, and the coupling parameter v is positive. If the 'kinetic potential' bar{f}(s) associated with f(x) is defined by the transformation: bar{f}(s) = F'(v), s = F(v)-vF'(v),then f can be reconstructed from F by the sequence: f^{[n+1]} = bar{f} o bar{f}^{[n]^{-1}} o f^{[n]}. Convergence is proved for special classes of potential shape; for other test cases it is demonstrated numerically. The seed potential shape f^{[0]} need not be 'close' to the limit f.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-07T17:34:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanics",
      "functional inversion",
      "schroedinger hamiltonian",
      "ground-state eigenvalue",
      "kinetic potential"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}