{
  "id": "quant-ph/0508005",
  "version": "v1",
  "published": "2005-07-31T21:58:41.000Z",
  "updated": "2005-07-31T21:58:41.000Z",
  "title": "Star-quantization of an infinite wall",
  "authors": [
    "Sergei Kryukov",
    "Mark A. Walton"
  ],
  "comment": "6 pages, 0 figures, submitted to Canadian Journal of Physics, special issue for the proceedings of Canada Theory 1 (6/05, UBC)",
  "journal": "Can. J. Phys.84:557-563, 2006",
  "doi": "10.1139/P06-017",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata pointed out that, surprisingly, its stationary-state Wigner function does not obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue) equation. We review our recent work on this problem, that treats the infinite wall as the limit of a Liouville potential. Also included are some new results: (i) we show explicitly that the Wigner-Weyl transform of the usual density matrix is the physical solution, (ii) we prove that an effective-mass treatment of the problem is equivalent to the Liouville one, and (iii) we point out that self-adjointness of the operator Hamiltonian requires a boundary potential, but one different from that proposed by Dias and Prata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-31T21:58:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite wall",
      "star-quantization",
      "usual density matrix",
      "infinite potential wall",
      "stationary-state wigner function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Canadian Journal of Physics",
      "year": 2006,
      "month": "Jun",
      "volume": 84,
      "number": "6-7",
      "pages": 557
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 707700,
      "adsabs": "2006CaJPh..84..557K"
    }
  }
}