Symmetry adapted harmonic oscillator functions

Quantum mechanical excited energy states of two- or three-dimensional harmonic oscillators are highly degenerate. A general method is presented to calculate the symmetry adapted quantum mechanical oscillator functions with respect to the symmetry group of the oscillator. In the special case of the tetrahedral symmetry group the method is demonstrated by detailed formulas for the two- and three-dimensional case. A computer program is also available. The method can easily be modified for other symmetry groups.