{
  "id": "quant-ph/0411084",
  "version": "v1",
  "published": "2004-11-11T18:38:05.000Z",
  "updated": "2004-11-11T18:38:05.000Z",
  "title": "Exact quantization of nonsolvable potentials: the role of the quantum phase beyond the semiclassical approximation",
  "authors": [
    "A. Matzkin"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "Semiclassical quantization is exact only for the so called \\emph{solvable} potentials, such as the harmonic oscillator. In the \\emph{nonsolvable} case the semiclassical phase, given by a series in $\\hbar$, yields more or less approximate results and eventually diverges due to the asymptotic nature of the expansion. A quantum phase is derived to bypass these shortcomings. It achieves exact quantization of nonsolvable potentials and allows to obtain the quantum wavefunction while locally approaching the best pre-divergent semiclassical expansion. An iterative procedure allowing to implement practical calculations with a modest computational cost is also given. The theory is illustrated on two examples for which the limitations of the semiclassical approach were recently highlighted: cold atomic collisions and anharmonic oscillators in the nonperturbative regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-11T18:38:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum phase",
      "nonsolvable potentials",
      "semiclassical approximation",
      "cold atomic collisions",
      "modest computational cost"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph.11084M"
    }
  }
}