Problem 7 Consider a rotor with moment of inertia is I, that rotates freely around the z-axis. Define o to be the variable Euler angle of the rotor in the z-y plane. (a) Find the energy eigenvalues and the corresponding normalized eigenfunctions. (b) At time t = 0, the rotor is described by a wavefunction V(6,t = 0) = Asin'o with A a constant. Find the wavefunction V(6, t) at time t>0. Hint: You may want to consider the classical Hamiltonian of an analog classical problem as illustrated in the figure.

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Problem 4: Speed deamplifier. In the figure above on the right, block 1 of mass m1 slides along an x-axis on a frictionless floor at speed 4 m/sec.Then it undergoes a one-dimensional elastic collision with stationary block 2 of mass m2 = 2m1. Next, block 2 undergoes a one-dimensional elastic collision with stationary block 3 of mass mz = 4m1. What then is the speed of block 3? Answer: 16 m/sec or 1.78 m/sec.