1. (20 points) Consider a modified version of the Stern-Gerlach experiment. Rather than send- ing spin-1/2 particles through a magnetic field, we put an unpolarized beam of spin-3/2 particles through a Stern-Gerlach apparatus as in the figure below. The unpolarized beam Sz = 3 2 SG *?? SGZ enters a SGz apparatus, and four beams come out. The polarized beam corresponding to Sz = 3/2 is then sent through an SGx apparatus. (a) (10 points) What fraction of particles entering the second apparatus exit with Sx 3/2? Sx = /2? Sx = -/2? Sx = -3/2? (b) (10 points) Suppose that, instead of sending the polarized Sz 3/2 beam into the SGx apparatus, we send the Sz = -/2 beam. Repeat part (a) for this case