{
  "annotation_id": "b29f1225-1cf6-46e8-b6b4-3ef0c905747f",
  "date_created": "2026-03-02T18:01:38.923000Z",
  "date_modified": "2026-03-02T18:01:38.923000Z",
  "file_hash": "f4ce8ffd7bcd84950b6f0078ecb21154291195e25be754fbad6ac76733e4af17",
  "private": false,
  "record": {
    "abstract": "It is shown, that oscillators on the sphere and the pseudosphere are related,\nby the so-called Bohlin transformation, with the Coulomb systems on the\npseudosphere. The even states of an oscillator yield the conventional Coulomb\nsystem on the pseudosphere, while the odd states yield the Coulomb system on\nthe pseudosphere in the presence of magnetic flux tube generating spin 1/2. A\nsimilar relation is established for the oscillator on the (pseudo)sphere\nspecified by the presence of constant uniform magnetic field $B_0$ and the\nCoulomb-like system on pseudosphere specified by the presence of the magnetic\nfield $\\frac{B}{2r_0}(|\\frac{x_3}{{\\bf x}}|-\\epsilon)$. The correspondence\nbetween the oscillator and the Coulomb systems the higher dimensions is also\ndiscussed.",
    "arxiv_id": "quant-ph/0006118",
    "authors": [
      "Armen Nersessian",
      "George Pogosyan"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "math-ph",
      "math.MP",
      "physics.atom-ph"
    ],
    "doi": "10.1103/PhysRevA.63.020103",
    "journal_ref": "Phys.Rev.A63:020103,2001",
    "title": "Relation of the oscillator and Coulomb systems on spheres and   pseudospheres",
    "url": "https://arxiv.org/abs/quant-ph/0006118"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8b035b9f-c570-4fc1-a849-8f9a52301bb3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}