{
  "annotation_id": "b96eab6d-04ab-47be-af8a-6a4d851657d0",
  "date_created": "2026-03-02T18:02:34.503000Z",
  "date_modified": "2026-03-02T18:02:34.503000Z",
  "file_hash": "bc777322ea5914b41093f7fa1b826d474fd0f45de29f5693ba2bf3282d41265b",
  "private": false,
  "record": {
    "abstract": "An exactly solvable position-dependent mass Schr\\\"odinger equation in two\ndimensions, depicting a particle moving in a semi-infinite layer, is\nre-examined in the light of recent theories describing superintegrable\ntwo-dimensional systems with integrals of motion that are quadratic functions\nof the momenta. To get the energy spectrum a quadratic algebra approach is used\ntogether with a realization in terms of deformed parafermionic oscillator\noperators. In this process, the importance of supplementing algebraic\nconsiderations with a proper treatment of boundary conditions for selecting\nphysical wavefunctions is stressed. Some new results for matrix elements are\nderived. Finally, the two-dimensional model is extended to two integrable and\nexactly solvable (but not superintegrable) models in three dimensions,\ndepicting a particle in a semi-infinite parallelepipedal or cylindrical\nchannel, respectively.",
    "arxiv_id": "quant-ph/0612094",
    "authors": [
      "C. Quesne"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "title": "More on an exactly solvable position-dependent mass Schroedinger   equation in two dimensions: Algebraic approach and extensions to three   dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0612094"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "102d3194-04bf-43c8-9364-415fbcc43b4a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}