Consider a system of a rigid rotator together with a uniform E-field directing along z-axis. So to calculate the perturbed energy and wavefunction we have to use perturbation theory. But the book said we can use non-degenerate one to calculate the result. I wonder why. It is because the original hamitonian and the perturbed one commute with Lz so that we are sure that the first term of the perturbed wavefunction must be the original unperturbed eigenfunction? Does it mean that there are no more physical quantities except Lz which could be certain if we are certain of its energy? Also, why do we use a linear combination of the degenerate eigenfunction for the first term of the perturbed wavefunction? I think it is becos we are not sure of how other physical quantities behave under the perturbed situation. What do you guys think?