Symmetry Algebra of the Planar Anisotropic Quantum Harmonic Oscillator   with Rational Ratio of Frequencies
  The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies 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. 
Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis and D. Lenis