{
  "annotation_id": "b5b223f4-f459-4d91-ad21-4a0eacb4e58a",
  "date_created": "2026-03-02T18:02:20.414000Z",
  "date_modified": "2026-03-02T18:02:20.414000Z",
  "file_hash": "a863315717bd29de80e05878a1b1c4b6fe4b47f71ba99cecb2136ca543c3f75d",
  "private": false,
  "record": {
    "abstract": "In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of\nquantum mechanics), we consider a single quantum particle moving freely in one\ndimension, except for the presence of one infinite potential wall. Dias and\nPrata pointed out that, surprisingly, its stationary-state Wigner function does\nnot obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue)\nequation. We review our recent work on this problem, that treats the infinite\nwall as the limit of a Liouville potential. Also included are some new results:\n(i) we show explicitly that the Wigner-Weyl transform of the usual density\nmatrix is the physical solution, (ii) we prove that an effective-mass treatment\nof the problem is equivalent to the Liouville one, and (iii) we point out that\nself-adjointness of the operator Hamiltonian requires a boundary potential, but\none different from that proposed by Dias and Prata.",
    "arxiv_id": "quant-ph/0508005",
    "authors": [
      "Sergei Kryukov",
      "Mark A. Walton"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1139/P06-017",
    "journal_ref": "Can. J. Phys.84:557-563, 2006",
    "title": "Star-quantization of an infinite wall",
    "url": "https://arxiv.org/abs/quant-ph/0508005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "91b5e8d2-f545-4ce4-8861-00f4d967fd3e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}