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I've got a quick question on the Stern-Gerlach experiment. On page 182 in the description of it, it says that we would normally expect a “smearing” of the two lines that are deflected, but instead we just see two perfect lines…Do they expect it to blur because of the uncertainty princible such that we know the angular momentum in the z direction of the beams leaving, so the actual position of the parts of the beam shouldn't be known as well? The way I read it, they say the reason there isn't any smearing is because the angular momentum is quantized. Wouldn't this pose a problem for the uncertainty principle then, if we can get around the predicted “smearing” by giving it special quantized values, or am I just misunderstanding this?

From what I get about this, the smearing is predicted in terms of classical mechanics. This would be a result of the particles corresponding to each individual value for the m quantum number. However, in quantum mechanics we know that each particle has some manner of spin to it thus each particle is quantized in the z direction. As Yuichi showed us in class, whether they have spin up or spin down rotations determines whether they deflect up or down.

It would be smeared if the particles could have any value for their spin. The spin value determines how much the particle is deflected by the magnetic field. Since the spin is only 1/2 or -1/2, there are only two deflections that the particles could have.

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