2006/12/31 by A. M. Gavrilik, A. P. Rebesh · 8 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Annihilation #Creation and annihilation operators #Cutoff #Degeneracy (biology) #Energy (signal processing) #Mathematical physics #Momentum (technical analysis) #Nonlinear Waves and Solitons #Physics #Position (finance) #Quantum mechanics #cond-mat.stat-mech #hep-th #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1142/s0217732307022827
published as Mod.Phys.Lett.A22:949-960,2007 · 12 pages, 7 figures; v.2 misprints corrected, two references added, to appear in Mod.Phys.Lett.A
arxiv created 2007/02/08 · openalex publication_date 2007/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ≥ 1, at the real value[Formula: see text] of deformation parameter, as well as the occurrence of other degeneracies E n 1 = E n 1 + k , for k ≥ 2, at the corresponding values of q which depend on both n 1 and k; (ii) the position and momentum operators X and Pcommute on the state|n 1 > if q is fixed as [Formula: see text], 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 non-simple Lie algebra su(2) ⊕ u(1)whose nontrivial q-deformed commutation relation is: [J + , J - ] = 2J 0 q 2J 3 -1 where [Formula: see text] and [Formula: see text].