{
  "annotation_id": "00100634-5d4e-403b-bd0e-bbf40a59c82f",
  "date_created": "2026-03-02T18:02:20.632000Z",
  "date_modified": "2026-03-02T18:02:20.632000Z",
  "file_hash": "b34bf23c17989f259d0106da12f72c25fa3b40c2aa3860461edd7ce66c312448",
  "private": false,
  "record": {
    "abstract": "In this contribution I show that it is possible to construct\nthree-dimensional spaces of non-constant curvature, i.e. three-dimensional\nDarboux-spaces. Two-dimensional Darboux spaces have been introduced by Kalnins\net al., with a path integral approach by the present author. In comparison to\ntwo dimensions, in three dimensions it is necessary to add a curvature term in\nthe Lagrangian in order that the quantum motion can be properly defined. Once\nthis is done, it turns out that in the two three-dimensional Darboux spaces,\nwhich are discussed in this paper, the quantum motion is similar to the\ntwo-dimensional case. In $\\threedDI$ we find seven coordinate systems which\nseparate the Schr\\\"odinger equation. For the second space, $\\threedDII$, all\ncoordinate systems of flat three-dimensional Euclidean space which separate the\nSchr\\\"odinger equation also separate the Schr\\\"odinger equation in\n$\\threedDII$. I solve the path integral on $\\threedDI$ in the $(u,v,w)$-system,\nand on $\\threedDII$ in the $(u,v,w)$-system and in spherical coordinates.",
    "arxiv_id": "quant-ph/0511135",
    "authors": [
      "Christian Grosche"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1134/S1063778807030131",
    "journal_ref": "Phys.Atom.Nucl.70:537-544,2007",
    "title": "Path Integral Approach for Spaces of Non-constant Curvature in Three   Dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0511135"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ec786180-a25a-492d-b031-3ae3e7bf86a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}