dorsal/arxiv
View SchemaNonlinear 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
| Authors | Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis, D. Lenis |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9412003 |
| URL | https://arxiv.org/abs/nucl-th/9412003 |
Abstract
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$_3^{(2)}$.
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"abstract": "The symmetry algebra of the two-dimensional anisotropic quantum harmonic\noscillator with rational ratio of frequencies, which is characterizing\n``pancake\u0027\u0027 nuclei, is identified as a non-linear extension of the u(2)\nalgebra. The finite dimensional representation modules of this algebra are\nstudied and the energy eigenvalues are determined using algebraic methods of\ngeneral applicability to quantum superintegrable systems. For labelling the\ndegenerate states an ``angular momentum\u0027\u0027 operator is introduced, the\neigenvalues of which are roots of appropriate generalized Hermite polynomials.\nIn the special case with frequency ratio 2:1 the resulting algebra is\nidentified as the finite W algebra W$_3^{(2)}$.",
"arxiv_id": "nucl-th/9412003",
"authors": [
"Dennis Bonatsos",
"C. Daskaloyannis",
"P. Kolokotronis",
"D. Lenis"
],
"categories": [
"nucl-th"
],
"title": "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\u0027\u0027 nuclei",
"url": "https://arxiv.org/abs/nucl-th/9412003"
},
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