Chapter 2 Representations

In the last chapter we learned something about the structure of the groups themselves, but we are really interested in how the symmetry groups act on the eigenstates of a physical Hamiltonian. The set of states corresponding to a given eigenvalue of degeneracy l forms a vector space of dimension l. The result of applying the symmetry operation to any of these states gives a state with the same energy eigenvalue, and thus a state in the same l-dimensional vector space. The symmetry acts linearly on the states,