3. It turns out that the polarization of a photon is related to its angular momentum J. In the IhHO} basis, we can write the z-component of the angular momentum as - h 0 I2 _' [0 _) ' (a) Is this operator hermitian? Do you expect it to be {and why or why not)? (b) What are the eigenvalues and eigenstates nsz? (e) If you were to make a measurement of j; on a photon in the state If), what are the possible results you could measure, and what is the probability of getting each? ((1) Calculate (L) for the state Ir) 4. In an experiment, a photon propagates along the optic axis (the x-axis in this case) of a quartz crystal. The Hamiltonian for this system, in the |h)|a) basis, is given by A 0 I'Ea H > [1. El] 0 )