Introduction to Mathematical Physics/N body problem in quantum mechanics/Exercises

Give the name of the symmetry group molecule belongs to. Parametrize the vibrations of molecule and expand it in a sum of irreducible representations. Propose a basis for the study of molecule different from those presented at section secnnne. Find the eigenstates as well as their energies of a system constituted by an electron in a square box of side (potential zero for and , potential infinite elsewhere). What happens if to this potential is added a perturbation of value on a quarter of the box ( and )? Calculate by perturbation the new energies and eigenvectors. Would symmetry considerations have permitted to know in advance the eigenvectors?