{
  "annotation_id": "94be657e-7e26-46bb-85cb-2533b23aa05e",
  "date_created": "2026-03-02T18:01:58.862000Z",
  "date_modified": "2026-03-02T18:01:58.862000Z",
  "file_hash": "951b5fd2cf024a78a20c99f1e88a4db960250b3af1c97171e0892755af115283",
  "private": false,
  "record": {
    "abstract": "For any central potential V in D dimensions, the angular Schroedinger\nequation remains the same and defines the so called hyperspherical harmonics.\nFor non-central models, the situation is more complicated. We contemplate two\nexamples in the plane: (1) the partial differential Calogero\u0027s three-body model\n(without centre of mass and with an impenetrable core in the two-body\ninteraction), and (2) the Smorodinsky-Winternitz\u0027 superintegrable harmonic\noscillator (with one or two impenetrable barriers). These examples are solvable\ndue to the presence of the barriers. We contemplate a small complex shift of\nthe angle. This creates a problem: the barriers become \"translucent\" and the\nangular potentials cease to be solvable, having the sextuple-well form for\nCalogero model and the quadruple or double well form otherwise. We mimic the\neffect of these potentials on the spectrum by the multiple, purely imaginary\nsquare wells and tabulate and discuss the result in the first nontrivial\ndouble-well case.",
    "arxiv_id": "quant-ph/0304046",
    "authors": [
      "Miloslav Znojil"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/28/311",
    "journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 7825-7838",
    "title": "PT symmetric models in more dimensions and solvable square-well versions   of their angular Schroedinger equations",
    "url": "https://arxiv.org/abs/quant-ph/0304046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d771e676-ef9a-4cd9-9f25-c880153250e4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}