{
  "id": "1503.05101",
  "version": "v1",
  "published": "2015-03-17T15:49:12.000Z",
  "updated": "2015-03-17T15:49:12.000Z",
  "title": "A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator",
  "authors": [
    "Alberto Enciso",
    "David Hartley",
    "Daniel Peralta-Salas"
  ],
  "comment": "12 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We prove that, given any finite link L in R^3, there is a high energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-17T15:49:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic oscillator",
      "knotted zeros",
      "high energy complex-valued eigenfunction",
      "nodal set contains",
      "quantum system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}