{
  "id": "1210.5055",
  "version": "v1",
  "published": "2012-10-18T08:49:09.000Z",
  "updated": "2012-10-18T08:49:09.000Z",
  "title": "Curvature-dependent formalism, Schrödinger equation and energy levels for the harmonic oscillator on three-dimensional spherical and hyperbolic spaces",
  "authors": [
    "José F. Cariñena",
    "Manuel F. Rañada",
    "Mariano Santander"
  ],
  "journal": "J. Phys. A: Math. Theor. 45, 265303 (14pp) (2012)",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\\k^3$ ($\\kappa>0$) and $H_k^3$ ($\\kappa<0$), is studied. The curvature $\\k$ is considered as a parameter and then the radial Schr\\\"odinger equation becomes a $\\k$-dependent Gauss hypergeometric equation that can be considered as a $\\k$-deformation of the confluent hypergeometric equation that appears in the Euclidean case. The energy spectrum and the wavefunctions are exactly obtained in both the three-dimensional sphere $S_\\k^3$ ($\\kappa>0$) and the hyperbolic space $H_k^3$ ($\\kappa<0$). A comparative study between the spherical and the hyperbolic quantum results is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-18T08:49:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q05",
      "81R12",
      "81U15",
      "34B24"
    ],
    "keywords": [
      "hyperbolic space",
      "curvature-dependent formalism",
      "schrödinger equation",
      "energy levels",
      "three-dimensional spherical"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/45/26/265303",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2012,
      "month": "Jul",
      "volume": 45,
      "number": 26,
      "pages": 265303
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1207179,
      "adsabs": "2012JPhA...45z5303C"
    }
  }
}