Knowledge Bank

As $Melvin1$ in particular has shown, for point symmetry groups the projection operator technique provides a powerful tool to obtain symmetry adapted functions or coordinates, e.g., in molecular electronic or vibrational problems. In constructing the projection operators involved, which is in principle a straight forward matter, two problems generally arise. The first one concerns the essential non-uniqueness of degenerate representations and the other the possible simplification of the operator. Although both questions are closely related, it is often of physical significance to put the emphasis not on the simplification in the first place but rather on the specification of the degenerate representations. This can be done by selecting some subgroup (of the original group)of symmetry low enough to lift the degeneracies partly or completely and adapting the projection operators to this choice.”