{
  "id": "quant-ph/0612122",
  "version": "v2",
  "published": "2006-12-14T19:36:14.000Z",
  "updated": "2007-02-08T20:19:23.000Z",
  "title": "A q-Oscillator with 'Accidental' Degeneracy of Energy Levels",
  "authors": [
    "A. M. Gavrilik",
    "A. P. Rebesh"
  ],
  "comment": "12 pages, 7 figures; v.2 misprints corrected, two references added, to appear in Mod.Phys.Lett.A",
  "journal": "Mod.Phys.Lett.A22:949-960,2007",
  "doi": "10.1142/S0217732307022827",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP",
    "nucl-th"
  ],
  "abstract": "We study main features of the exotic case of q-deformed oscillators (so-called Tamm-Dancoff cutoff oscillator) and find some special properties: (i) degeneracy of the energy levels E_{n_1} = E_{n_1+1}, n_1\\ge 1, at the {\\em real value} q=\\sqrt{\\frac{n_1}{n_1+2}} of deformation parameter, as well as the occurrence of other degeneracies E_{n_1} = E_{n_1+k}, for k \\ge 2, at the corresponding values of q which depend on both n_1 and k; (ii) the position and momentum operators X and P {\\em commute on the state} |m> if q is fixed as q=\\frac{m}{m+1}, that implies unusual uncertainty relation; (iii) two commuting copies of the creation, annihilation, and number operators of this q-oscillator generate the corresponding q-deformation of the {\\em non-simple} Lie algebra su(2)\\oplus u(1) whose nontrivial q-deformed commutation relation is: [ J_+, J_- ] = 2 J_0 q^{2J_3-1} where J_0\\equiv \\frac12 (N_1-N_2) and J_3\\equiv \\frac12 (N_1+N_2).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-08T20:19:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Fd",
      "05.30.Pr",
      "02.20.Uw"
    ],
    "keywords": [
      "energy levels",
      "degeneracy",
      "implies unusual uncertainty relation",
      "accidental",
      "tamm-dancoff cutoff oscillator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 734884
    }
  }
}