Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1994-12-02
Physics
Nuclear Physics
Nuclear Theory
11 pages, LaTeX, e-mails bonat@cyclades.nrcps.ariadne-t.gr, daskaloyanni@olymp.ccf.auth.gr
Scientific paper
The 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$_3^{(2)}$.
Bonatsos Dennis
Daskaloyannis Costas
Kolokotronis P.
Lenis D.
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