Two particles of mass m are attached to the ends of a massless rigid rod of length a. The...

Two particles of mass m are attached to the ends of a massless rigid rod of length a. The system is free to rotate in three dimensions about the center (but the centre point itself is fixed).

(a) show that the allowed energies of this rigid rod are

 for n = 0, 1, 2,...

Hint: First express the (classical) energy in terms of the total angular momentum.

(b) What are the normalized eigenfunctions for this system? What is the degeneracy of the nth energy level?