{
  "id": "0709.3697",
  "version": "v1",
  "published": "2007-09-24T07:41:12.000Z",
  "updated": "2007-09-24T07:41:12.000Z",
  "title": "On the harmonic oscillator on the Lobachevsky plane",
  "authors": [
    "P. Stovicek",
    "M. Tusek"
  ],
  "comment": "to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler)",
  "doi": "10.1134/S1061920807040152",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential $V(r)=(a^2\\omega^2/4)sinh(r/a)^2$ where $a$ is the curvature radius and $r$ is the geodesic distance from a fixed center. Thus the potential is rotationally symmetric and unbounded likewise as in the Euclidean case. The eigenvalue equation leads to the differential equation of spheroidal functions. We provide a basic numerical analysis of eigenvalues and eigenfunctions in the case when the value of the angular momentum, $m$, equals 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-24T07:41:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lobachevsky plane",
      "harmonic oscillator",
      "angular momentum",
      "basic numerical analysis",
      "curvature radius"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Russian Journal of Mathematical Physics",
      "year": 2007,
      "month": "Dec",
      "volume": 14,
      "number": 4,
      "pages": 493
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007RJMP...14..493S"
    }
  }
}