{
  "id": "0706.4127",
  "version": "v1",
  "published": "2007-06-28T00:39:49.000Z",
  "updated": "2007-06-28T00:39:49.000Z",
  "title": "Semiclassical Density of States for the Quantum Asymmetric Top",
  "authors": [
    "Alfonso F. Agnew",
    "Alain Bourget"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the quantization of a rotating rigid body, a {\\it top,} one is concerned with the Hamiltonian operator $L_\\alpha=\\alpha_0^2 L_x^2 + \\alpha_1^2 L_y^2 + \\alpha_2^2 L_z^2,$ where $\\alpha_0 < \\alpha_1 <\\alpha_2.$ An explicit formula is known for the eigenvalues of $L_\\alpha$ in the case of the spherical top ($\\alpha_1 = \\alpha_2 = \\alpha_3$) and symmetrical top ($\\alpha_1 = \\alpha_2 \\neq \\alpha_3$) \\cite{LL}. However, for the asymmetrical top, no such explicit expression exists, and the study of the spectrum is much more complex. In this paper, we compute the semiclassical density of states for the eigenvalues of the family of operators $L_\\alpha=\\alpha_0^2 L_x^2 + \\alpha_1^2 L_y^2 + \\alpha_2^2 L_z^2$ for any $\\alpha_0 < \\alpha_1 <\\alpha_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-28T00:39:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q50",
      "81Q10"
    ],
    "keywords": [
      "semiclassical density",
      "quantum asymmetric",
      "explicit expression",
      "rotating rigid body",
      "hamiltonian operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4127A"
    }
  }
}