Open AccessNonlinear extension of the u(3) algebra as the symmetry algebra of the three-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies and the Nilsson model
Author(s) -
Dennis Bonatsos,
C. Daskaloyannis,
P. Kolokotronis,
D. Lenis
Publication year - 2020
Publication title -
hnps advances in nuclear physics
Language(s) - English
Resource type - Journals
eISSN - 2654-0088
pISSN - 2654-007X
DOI - 10.12681/hnps.2891
Subject(s) - degenerate energy levels , current algebra , physics , harmonic oscillator , quantum mechanics , quantum algebra , mathematical physics , algebra over a field , quantum , coherent states , connection (principal bundle) , mathematics , pure mathematics , geometry
The symmetry algebra of the N-dimensional anisotropic quantum har- monic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim oscillator is studied in more detail, because of its relevance in the description of superdeformed nuclei and nuclear and atomic clusters. In this case the symmetry algebra turns out to be a nonlinear extension of the u(3) algebra. A generalized angular momentum operator useful for labeling the degenerate states is constructed, clarifying the connection of the present formalism to the Nilsson model.