Spin Prob 1

Problem 1:(Added by Hang Chen's group)

P is a beam of atoms with spin quantum number 1/2 and zero orbital angular momentum, all with angular momentum ${\frac {\hbar }{2}}$ along the x axis. Q is a beam of similar but unpolarised atoms.

(a) What's the spin state function of P in terms of $\alpha$ and $\beta$, the eigenfunctions of $S_{z}$