Assume a Stern-Gerlach apparatus oriented along the z-axis acts as a measurement on the basis of the z-component of a spin-1/2 particle's spin. The incoming particles travel along the y-axis and have randomly aligned magnetic moments / spins.
If we focus on one single particle from the incoming beam, say with spin pointed along the x-axis, will its spin be reoriented into the $\pm$ z direction when it passes through the magnet? Is it incorrect to assume the spin state of one of the particles before it passes through a magnet?
I think each incoming particle's spin is supposed to be treated as a superposition of states. I suppose treating an incoming spin as being in some superposition of $\pm$ z states could account for any orientation of the spin, including x- or y-components. Is this the case? And then the measurement causes the particle's hbar/2 units of angular momentum to be assigned to either $\pm$ z?