{
  "id": "1703.04091",
  "version": "v1",
  "published": "2017-03-12T10:00:17.000Z",
  "updated": "2017-03-12T10:00:17.000Z",
  "title": "Self-adjoint extensions and unitary operators on the boundary",
  "authors": [
    "Paolo Facchi",
    "Giancarlo Garnero",
    "Marilena Ligabò"
  ],
  "comment": "16 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We establish a bijection between the self-adjoint extensions of the Laplace operator on a bounded regular domain and the unitary operators on the boundary. Each unitary encodes a specific relation between the boundary value of the function and its normal derivative. This bijection sets up a characterization of all physically admissible dynamics of a nonrelativistic quantum particle confined in a cavity. More- over, this correspondence is discussed also at the level of quadratic forms. Finally, the connection between this parametrization of the extensions and the classical one, in terms of boundary self-adjoint operators on closed subspaces, is shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-12T10:00:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35J25",
      "47A07"
    ],
    "keywords": [
      "unitary operators",
      "self-adjoint extensions",
      "nonrelativistic quantum particle",
      "boundary self-adjoint operators",
      "unitary encodes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}