The isotropic threedimensional harmonic oscillator is described by the Schrödinger equation in units such that The wavefunction is separable in Cartesian coordinates giving a product of three onedimensional oscillators with total energies More interesting is the solution separable in spherical polar coordinates with the radial function Here is an associated Laguerre polynomial a spherical harmonic and a normalization constant The energy levels are then given by being fold degenerate For a given angular momentum quantum number the possible values of are The conventional code is used to label angular momentum states with representing This Demonstration shows contour plots in the plane for the lowerenergy eigenfunctions with to For the eigenfunctions are complex In all cases the real parts of are drawn The wavefunctions are positive in the blue regions and negative in the white regions The radial functions are also plotted as well as an energylevel diagram with each dash representing the degenerate set of eigenstates for a given The pattern of degeneracies for a threedimensional oscillator implies invariance under an SU3 Lie algebra the same as the gauge group describing the color symmetry of strong interactions