Symmetry algebra of the anisotropic harmonic oscillator with commensurate frequencies
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.
Publication Source (Journal or Book title)
Journal of Physics A: Mathematical and General
Rosensteel, G., & Draayer, J. (1989). Symmetry algebra of the anisotropic harmonic oscillator with commensurate frequencies. Journal of Physics A: Mathematical and General, 22 (9), 1323-1327. https://doi.org/10.1088/0305-4470/22/9/021