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

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Exercice:

Give the name of the symmetry group molecule belongs to.

Exercice:

Parametrize the vibrations of molecule and expand it in a sum of irreducible representations.

Exercice:

Propose a basis for the study of molecule different from those presented at section secnnne.

Exercice:

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?