1. Spherical rotator is a two-degree of freedom physical system that can execute general rotational motion characterized by the two angles O and o of the polar spherical coordinate system; its classical Hamiltonian function is M' H = 21 (1) where M is the angular momentum vector and / is the moment of inertia. The Hamiltonian operator of the spherical rotator has the form M2 1212 H = (2) 21 21 where 12 is the operator of the square of angular momentum discussed in class as well as in Problem 3 of Assignment # 5. (a) List all the physical quantities that can simultaneously have definite values. (b) Determine the stationary state wave functions and energy levels of the spherical rotator. What is their degeneracy and parity? (c) In a state with the wave function y(0, p) = Ccos2 0 (3) determine the probability of different values of the angular momentum and its projection, their average values and the dispersions. For your information, relevant spherical functions have the form 21 + 1 1 d' P(cos 0), P(x) = 4x 21! art - 1y'. (4)