{
  "annotation_id": "e1ff33a3-ff3e-48c7-bb6b-990b52336fee",
  "date_created": "2026-03-02T18:02:13.631000Z",
  "date_modified": "2026-03-02T18:02:13.631000Z",
  "file_hash": "b18eb37892e6adcfa4d5a688041d0079767a9949df6c7267f82ed052eafce6f6",
  "private": false,
  "record": {
    "abstract": "In this paper the Feynman path integral technique is applied to\ntwo-dimensional spaces of non-constant curvature: these spaces are called\nDarboux spaces $\\DI$--$\\DIV$. We start each consideration in terms of the\nmetric and then analyze the quantum theory in the separable coordinate systems.\nThe path integral in each case is formulated and then solved in the majority of\ncases, the exceptions being quartic oscillators where no closed solution is\nknown. The required ingredients are the path integral solutions of the linear\npotential, the harmonic oscillator, the radial harmonic oscillator, the\nmodified P\\\"oschl--Teller potential, and for spheroidal wave-functions,\nrespectively. The basic path integral solutions, which appear here in a\ncomplicated way, have been developed in recent work and are known. The final\nsolutions are represented in terms of the corresponding Green\u0027s functions and\nthe expansions into the wave-functions, respectively. We also sketch some\nlimiting cases of the Darboux spaces, where spaces of constant negative and\nzero curvature emerge.",
    "arxiv_id": "quant-ph/0411199",
    "authors": [
      "Christian Grosche"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1134/S1063779606030051",
    "journal_ref": "Phys.Part.Nucl. 37 (2006) 368-389",
    "title": "Path Integration on Darboux Spaces",
    "url": "https://arxiv.org/abs/quant-ph/0411199"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "07913399-76b8-4b1f-aa9b-f27992e6facf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}