Nonlinear extension of the u(2) algebra as the symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies and ``pancake'' nuclei

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dc.creatorBonatsos, Dennis
dc.creatorDaskaloyannis, C.
dc.creatorKolokotronis, P.
dc.creatorLenis, D.
dc.date1994-12-02
dc.date.accessioned2026-07-07T05:41:24Z
dc.date.available2026-07-07T05:41:24Z
dc.descriptionThe symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems. For labelling the degenerate states an ``angular momentum'' operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polynomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W$_3^{(2)}$.
dc.description11 pages, LaTeX, e-mails bonat@cyclades.nrcps.ariadne-t.gr, daskaloyanni@olymp.ccf.auth.gr
dc.identifierhttps://arxiv.org/abs/nucl-th/9412003
dc.identifierhttp://arxiv.org/abs/nucl-th/9412003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/82557
dc.subjectNuclear Theory
dc.titleNonlinear extension of the u(2) algebra as the symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies and ``pancake'' nuclei
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