Characters are quantum numbers

Abstract

Character tables represent an invaluable tool for applications of group theory in physics and chemistry. They are useful, among other applications, to carry out the projection of functions which later on constitute the basis to simplify the calculations and establish the selection rules. However, the physical interpretation of the character tables as quantum numbers is not visible. In this contribution we prove that the characters are indeed conserved quantities associated with the discrete symmetry of a molecule. In the process, the eigenfunction method of symmetry projection emerges in natural form, an approach not discussed in traditional textbooks. A non trivial example involving the octahedral group ${\cal O}_h$ is presented.