A. Consider a system of 2 particles: particle 1 has spin 1, and particle 2 has spin 1/2. Let S be the total angular momentum operator of the two particles, where the eigenvalues of S^2 and Sz are
^2s(s+1) and ms, respectively. The particles are in the state s= 3/2 and ms = 1/2.
Calculate the wave function |s = 3/2 ms = 1/2> as a linear combination of the wave functions |m1s m2s>, where m1s is the z component of the spin of particle 1, and m2s is the z component of the spin of particle 2.
b. Find the probabilities that the z component of the spin of particle 1 is
i) m1s = +1
ii) m1s = 0
iii) m1s = -1