{
  "id": "0901.2843",
  "version": "v1",
  "published": "2009-01-19T13:20:17.000Z",
  "updated": "2009-01-19T13:20:17.000Z",
  "title": "Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics",
  "authors": [
    "Vladimir Rabinovich",
    "Steffen Roch"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\\\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\\\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-19T13:20:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "47B39"
    ],
    "keywords": [
      "essential spectra",
      "quantum mechanics",
      "exponential estimates",
      "eigenfunctions",
      "square root klein-gordon operators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/42/38/385207",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Sep",
      "volume": 42,
      "number": 38,
      "pages": 385207
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42L5207R"
    }
  }
}