Hi everyone,

I'm really sorry about this question - I've watched videos on the Stern-Gerlach experiment, but I can't seem to understand the gap in the deflection caused by the quantisation - my head is stuck in the classical understanding and I'm trying to understand why it really happens.

In the Stern-Gerlach experiment a stream of silver atoms is sent through a magnetic field oriented in the Z-direction. Before they enter the magnetic field, they are oriented randomly, and hence have a magnetic moment which is randomly oriented relative to the magnetic field. These magnetic moments are shown to be quantised to -h-bar/2.

I might have misunderstood something in the previous part, but here is where my confusion lies. My understanding is that the magnetic moment caused by the intrinsic spin is a vector in xyz, and I keep getting told to think about the magnetic moment like a needle in a compass. My understanding is the needle will align with the magnetic field as that is the lowest energy state. However, I'm not sure what's going on with the atom - is its magnetic moment caused by its instrinsic spin lining up along the z-axis of the magnetic field? I don't know if this is the case, because I was told that if you then attach another Stern-Gerlach machine in the x-axis in the spot where the spin-up atoms get deflected, they would then have a 50/50 chance to get deflected either up or down in the x-direction. However, my (classical) understanding is that if the magnetic moment had already been selected to be plus/negative in the z-direction by the first SG machine, then the magnetic moment would then be altered again and be pointing in the -x-direction. The whole thing collapses in that if the atom was re-orienting itself with the magnetic field, it would only show up in one place?

The only way now that I can understand it is that the atom has a quantised magnetic moment caused by its intrinsic spin in every axis regardless of its orientation w.r.t that axis in real space. By this I mean that in the x-direction it has a /-h-bar/2 magnitude, as well as in the y-direction and the z-direction.

I'm sorry I'm not the best at explaining myself and I'm very confused about this particular idea. Could someone please help untangle me?