The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. What is theoretically predicted to happen for electron beams?
[Physics] predicted to happen for electron beams in the Stern-Gerlach experiment
angular momentumexperimental-physicsquantum mechanicsquantum-electrodynamics
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This is a crucial aspect of Stern-Gerlach which is usually omitted from simple descriptions. To see the spin splitting cleanly, you want a massive neutral atom with an unpaired electron. Silver has an unpaired 5s electron, and all others are paired. The 5s electron is in a zero orbital angular momentum state, so as far as the magnetic response is concerned, only the spin changes in different fields.
You use a massive neutral object containing an unpaired S-electron, so that you only split the spin state in the B-field gradient, you don't muck around with orbital magnetic moment inside the atom, or for the particle as a whole. The rest of the silver atom is there to make sure that the only difference in deflection is due to the spin of the outer electron only.
For free electrons, the spin and orbital magnetic moment are related by the Dirac equation, and you can't make the splitting caused by the two different. This is the weird degeneracy in Landau levels, where the spin-splitting is exactly equal to the orbital splitting. This means that the momentum deflections of an electron beam by a magnetic field gradient is always going to be comparable to the deflection due to the different spin states. So you don't split an electron beam cleanly into spin states using magnetic field gradients.
The inner shells of the silver are paired up, so that the electrons are rigid--- you can't mix the electron states in any of the inner orbitals. But the outer electron spin-1/2 makes two degenerate states (ignoring some infinitesimal coupling to the nuclear spin), so the Silver atom ends up being just a massive neutral object with a magnetic moment equal to the magnetic moment due to the spin of a free electron.
Wave function collapse is a change of wave function that we do at certain time of experimenting "by hand", "because we get new facts", as opposed to a change of wave function determined by past data and Schroedinger's equation. It is a fix for our inability to get the new fact purely from calculations. One such fact is detection of the atom at one of few possible beams or landing spots.
When the atom passes through magnetic field without interacting with position-revealing devices, we do not invoke collapse, because we have no reason to - it is fine evolving the wave function just using the Schroedinger's equation there.
When the atom is detected at a screen and we get new information about its position (and its spin state), this is more than calculated wave function implies, and this allows us to update the wave function we got from Schroedinger's equation using the new fact.
Best Answer
Electron beams cannot be split by a stern Gerlach apparatus, because the spin splitting and the orbital splitting cannot be practically separated. The orbital splitting in a constant magnetic field is exactly of the same magnitude as the spin splitting, meaning that the spin anti-aligned electron in a given Landau level is more or less precisely degenerate with the spin aligned electron in the previous Landau level. This means that you can't separate the velocity deflection of the electron from the spin deflection.
This is why Stern Gerlach experiments are only done on atomic beams. There is no simple practical known way to correct for this.