I'm currently taking a first course in quantum mechanics and we just recently introduced generalized angular momentum. Now, take the special case of a spin-1/2 particle. If i understood this correctly there are two possibilities spin up: ms = 1/2 , and spin down ms = -1/2 , this comes from the fact that ms can take on the values +s,..-s where s is the spin quantum number. The eigenvalues of the SZ operator are ms[itex]\hbar[/itex], so these are the values the spin can take on when measured along the Z axis. Now this is what confuses me, what is meant by measuring the spin "along the Z axis" or along any axis for that matter, is this some sort of projection of the spin on the Z axis? What bothers me is i think of spin as some property of the particle, its either up or down, so whats with the measurement along some axis. Whats the purpose of this, cant we just say that its up or down and be done with it? Hope i made some sense of what confuses me, lol.