A q-Oscillator with 'Accidental' Degeneracy of Energy Levels

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dc.creatorGavrilik, A. M.
dc.creatorRebesh, A. P.
dc.date2006-12-14
dc.date2007-02-08
dc.date.accessioned2026-07-07T10:22:50Z
dc.date.available2026-07-07T10:22:50Z
dc.descriptionWe 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).
dc.description12 pages, 7 figures; v.2 misprints corrected, two references added, to appear in Mod.Phys.Lett.A
dc.identifierhttps://arxiv.org/abs/quant-ph/0612122
dc.identifierhttp://arxiv.org/abs/quant-ph/0612122
dc.identifierMod.Phys.Lett.A22:949-960,2007
dc.identifierdoi:10.1142/S0217732307022827
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/175656
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectNuclear Theory
dc.titleA q-Oscillator with 'Accidental' Degeneracy of Energy Levels
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