{
  "id": "1205.5941",
  "version": "v2",
  "published": "2012-05-27T06:45:14.000Z",
  "updated": "2012-09-07T16:06:43.000Z",
  "title": "Momentum operators on graphs",
  "authors": [
    "Pavel Exner"
  ],
  "comment": "AMSTeX, 14 pages, minor improvements, to appear in Fritz Gesztesy Festschrift",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "abstract": "We discuss ways in which momentum operators can be introduced on an oriented metric graph. A necessary condition appears to the balanced property, or a matching between the numbers of incoming and outgoing edges; we show that a graph without an orientation, locally finite and at most countably infinite, can made balanced oriented \\emph{iff} the degree of each vertex is even. On such graphs we construct families of momentum operators; we analyze their spectra and associated unitary groups. We also show that the unique continuation principle does not hold here.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-07T16:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q35",
      "47E05",
      "47D99"
    ],
    "keywords": [
      "momentum operators",
      "necessary condition appears",
      "unique continuation principle",
      "oriented metric graph",
      "construct families"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5941E"
    }
  }
}