Symmetry algebra of the anisotropic harmonic oscillator with commensurate frequencies
- 7 May 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (9) , 1323-1327
- https://doi.org/10.1088/0305-4470/22/9/021
Abstract
The symmetry algebra of the m-dimensional quantum anisotropic harmonic oscillator Hamiltonian H with commensurate frequencies is shown to be u(m). Each eigenspace of H carries a single irreducible representation of u(m). However, distinct eigenspaces can yield equivalent u(m) representations. The dynamical algebra is the non-compact symplectic algebra sp(m,r). For m+3, the anisotropic Hamiltonian is relevant to superdeformed nuclei.Keywords
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