Find the energy eigenstates for the system compute the

Question

The particle on a ring problem can be used to model electronic transitions in an aromatic hydrocarbon ring (benzene, naphthalene). For a particle on a ring, a particle of mass m is xed to move on a ring of radius a in the xy plane. The Hamiltonian of this system is H^ = ~ 2 2I d 2 d2 , I is the moment of inertia, I = ma 2 and  is the angle of the x-axis in the xy plane, which ranges from 0 to 2. a) Find the energy eigenstates for the system. b) Compute the normalization constant for these eigenstates. c) What is the boundary condition for this problem? d) What does this restrict the allowed energies of the system to be? e) What is the degeneracy of the energy levels