{
  "id": "1310.6651",
  "version": "v5",
  "published": "2013-10-24T15:55:21.000Z",
  "updated": "2014-09-04T18:10:22.000Z",
  "title": "Quantum dynamics of a particle constrained to lie on a surface",
  "authors": [
    "Gustavo de Oliveira"
  ],
  "comment": "Final version to appear in J. Math. Phys",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the strength of this constraining potential tends to infinity, the motion of this particle converges to a motion generated by a Hamiltonian over the surface superimposed by an oscillatory motion in the normal directions. Our result extend previous results by allowing magnetic potentials and more general constraining potentials.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-03T20:56:15.000Z",
      "comment": "35 pages; a comment after the main theorem was corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-09-04T18:10:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35Q40"
    ],
    "keywords": [
      "quantum dynamics",
      "euclidean space",
      "normal directions",
      "oscillatory motion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4895761",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Sep",
      "volume": 55,
      "number": 9,
      "pages": "092106"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55i2106D"
    }
  }
}