Can someone explain the basics of spin in the most simple terms? I have seen the formalism of it in an intro QM course but don't seem to connect how the matrices apply to reality. IN particular I am lacking a geometric view to the subject. So if we use the z axis matrix, we will find the wavefunction hence the probability of the electron in the spin up or down state. I have heard of the possibility of being in both spin and spin down state. Is that true? But when a measurement is down, it has to be in either one. I guess that in this way, it is like the other aspects of QM as well. What happens when we change to the x axis? The electron is still as it is but what has changed? It can only spin up or down wrt the x axis?