Symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies and {open_quotes}pancake{close_quotes} nuclei
- and others
The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing {open_quotes}pancake{close_quotes} nuclei, is identified as a nonlinear 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 labeling the degenerate states an {open_quotes}angular momentum{close_quotes} operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polyomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W{sup (2)}{sub 3}.
- OSTI ID:
- 374794
- Report Number(s):
- CONF-9304297--
- Journal Information:
- Bulletin of the American Physical Society, Journal Name: Bulletin of the American Physical Society Journal Issue: 2 Vol. 40; ISSN BAPSA6; ISSN 0003-0503
- Country of Publication:
- United States
- Language:
- English
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