{
  "id": "1502.00732",
  "version": "v1",
  "published": "2015-02-03T04:18:33.000Z",
  "updated": "2015-02-03T04:18:33.000Z",
  "title": "Nodal sets of Schrödinger eigenfunctions in forbidden regions",
  "authors": [
    "Yaiza Canzani",
    "John Toth"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "This note concerns the nodal sets of eigenfunctions of semiclassical Schr\\\"odinger operators acting on compact, smooth, Riemannian manifolds, with no boundary. We prove that if H is a separating hypersurface that lies inside the classically forbidden region, then H cannot persist as a component of the zero set of infinitely many eigenfunctions. In addition, on real analytic surfaces, we obtain sharp upper bounds for the number of intersections of the zero sets of the Schr\\\"odinger eigenfunctions with a fixed curve that lies inside the classically forbidden region.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-03T04:18:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nodal sets",
      "schrödinger eigenfunctions",
      "classically forbidden region",
      "zero set",
      "lies inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150200732C"
    }
  }
}