{
  "annotation_id": "2f3f62ef-2b02-4ab9-a48c-09e14be9673c",
  "date_created": "2026-03-02T18:01:59.974000Z",
  "date_modified": "2026-03-02T18:01:59.974000Z",
  "file_hash": "2212bedf9cdbefba13ab5c4a98ce6071eea4e39e56d9e9cfb44b44ef45973ba5",
  "private": false,
  "record": {
    "abstract": "We present quasi-analytical and numerical calculations of Gaussian wave\npacket solutions of the Schr\\\"odinger equation for two-dimensional infinite\nwell and quantum billiard problems with equilateral triangle, square, and\ncircular footprints. These cases correspond to N=3, N=4, and $N \\to \\infty$\nregular polygonal billiards and infinite wells, respectively. In each case the\nenergy eigenvalues and wavefunctions are given in terms of familiar special\nfunctions. For the first two systems, we obtain closed form expressions for the\nexpansion coefficients for localized Gaussian wavepackets in terms of the\neigenstates of the particular geometry. For the circular case, we discuss\nnumerical approaches. We use these results to discuss the short-time,\nquasi-classical evolution in these geometries and the structure of wave packet\nrevivals. We also show how related half-well problems can be easily solved in\neach of the three cases.",
    "arxiv_id": "quant-ph/0307070",
    "authors": [
      "M. A. Doncheski",
      "S. Heppelmann",
      "R. W. Robinett",
      "D. C. Tussey"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1119/1.1538574",
    "journal_ref": "Am. J. Phys. 71, 541 (2003)",
    "title": "Wave packet construction in two-dimensional quantum billiards:   Blueprints for the square, equilateral triangle, and circular cases",
    "url": "https://arxiv.org/abs/quant-ph/0307070"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "23c90d48-bf74-46cd-bd1e-7240b5ad07cf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}