{
  "annotation_id": "98938a52-45c6-460a-83bc-3e8360da561b",
  "date_created": "2026-03-02T18:02:50.813000Z",
  "date_modified": "2026-03-02T18:02:50.813000Z",
  "file_hash": "67bfd46a597eb831ccba74937c55059c33336dcc27b745d138639c83feb241f4",
  "private": false,
  "record": {
    "abstract": "We suggest an effective approach to separation of variables in the\nSchr\\\"odinger equation with two space variables. Using it we classify\ninequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\\\" odinger\nequations admit separation of variables. Besides that, we carry out separation\nof variables in the Schr\\\" odinger equation with the anisotropic harmonic\noscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of\ncoordinate systems providing its separability. Most of these coordinate systems\ndepend essentially on the form of the potential and do not provide separation\nof variables in the free Schr\\\" odinger equation ($V=0$).",
    "arxiv_id": "solv-int/9507003",
    "authors": [
      "Renat Z. Zhdanov",
      "Ihor V. Revenko",
      "Wilhelm I. Fushchych"
    ],
    "categories": [
      "solv-int",
      "hep-ph",
      "nlin.SI"
    ],
    "doi": "10.1063/1.531274",
    "title": "On the new approach to variable separation in the time-dependent   Schr\\\"odinger equation with two space dimensions",
    "url": "https://arxiv.org/abs/solv-int/9507003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "511f6367-1ab3-4834-bd41-414bc1af6b2d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}