{
  "id": "1006.1753",
  "version": "v1",
  "published": "2010-06-09T09:40:31.000Z",
  "updated": "2010-06-09T09:40:31.000Z",
  "title": "Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator",
  "authors": [
    "Sandro Graffi",
    "Lorenzo Zanelli"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr\\\"odinger propagator when the potential is quadratic at infinity. This construction is based on the geometric approach to the corresponding Hamilton-Jacobi equation and thus sidesteps the problem of the caustics generated by the classical flow. Moreover, a detailed study of the real phase function allows us to recover a WKB semiclassical approximation which necessarily involves the multivaluedness of the graph of the Hamiltonian flow past the caustics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-09T09:40:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric approach",
      "schrödinger propagator",
      "global parametrices",
      "fourier integral operators",
      "arbitrary large times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1753G"
    }
  }
}