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.