{
  "annotation_id": "b9e5d788-1fed-441a-a5c9-cff3c5730c91",
  "date_created": "2026-03-02T18:01:59.858000Z",
  "date_modified": "2026-03-02T18:01:59.858000Z",
  "file_hash": "7cc7540a0d2cdcabf6d51237954e243caba979b3911757d61fc237b22b7b4919",
  "private": false,
  "record": {
    "abstract": "We examine the quantum mechanical eigensolutions of the two-dimensional\ninfinite well or quantum billiard system consisting of a circular boundary with\nan infinite barrier or baffle along a radius. Because of the change in boundary\nconditions, this system includes quantized angular momentum values\ncorresponding to half-integral multiples of $\\hbar/2$. We discuss the resulting\nenergy eigenvalue spectrum and visualize some of the novel energy eigenstates\nfound in this system. We also discuss the density of energy eigenvalues,\n$N(E)$, comparing this system to the standard circular well. These two billiard\ngeometries have the same area (A=$\\pi R^2$), but different perimeters ($P=2\\pi\nR$ versus $(2\\pi + 2) R$), and we compare both cases to fits of $N(E)$ which\nmake use of purely geometric arguments involving only $A$ and $P$. We also\npoint out connections between the angular solutions of this system and the\nfamiliar pedagogical example of the one-dimensional infinite well plus\n$\\delta$-function potential.",
    "arxiv_id": "quant-ph/0307035",
    "authors": [
      "R. W. Robinett"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Eur. J. Phys. 24 (2003) 231",
    "title": "Quantum mechanics of the two-dimensional circular billiard plus baffle   system and half-integral angular momentum",
    "url": "https://arxiv.org/abs/quant-ph/0307035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bcde5821-1b3c-4452-9cc7-74db9a910fc2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}