A simple algorithm for the group theoretical classification of quantum states

Abstract

Here we present a simple and easily handled algorithm for the group theoretical classification of quantum states that although, it is implicit in a general group theory formulation, it is not presented the way it is discussed here, and which facilitates its application by non-specialists. It consists in finding the minimal set of symmetry operations needed to identify unequivocally the symmetry for each state and a direct calculation of the character of the representation expanded by the vector state. The algorithm allows simple and fast calculations of the symmetry properties, even for large symmetry groups and systems with many degrees of freedom. In particular the occurrence of accidental degeneracy is distinguished clearly using this method. In order to illustrate the application of the method, we discuss the classification of the vibrational states for two different molecular systems.