This Jared makes an interesting point. Everyone talks about the Stern Gerlach experiment as though you shoot a thin beam between two magnets, and it divides into two: so you get two splotches of silver on the glass plate. I pointed out in my last article that you really need to consider the thickness of the beam, as though it were the size of a pencil. Jared makes a slightly different point: he says that Stern and Gerlach used a collimated slit for their source, so the silver beam was really more fan-shaped than ray-like. And that the pattern on the glass plate was more of an ellipse than anything else:
But what I like most about his thesis was where he suggested a different way of setting up the magnetic field, so as to eliminate the DC component. He arranges four wires to create a perfect quadrupole field, like so:
He then asks the question: if you shoot a pencil beam of silver atoms through this magnetic field, what pattern do you get on the glass plate? If you think about it, it's a funny question.
It turns out Jared is some kind of monster mathematician, and he does a bunch of stuff that I don't really follow to end up with the nice result that the pencil beam becomes a donut on the glass plate.
Now that sounds right to me if you start out with a random, unpolarized beam. But it occurs to me: what if you have a polarized beam...one that's already been selected for spin in one direction by a conventional Stern-Gerlach filter? What pattern do you get in that case?
It's a question that I have to ask myself almost as a matter of put-up-or-shut-up: in my last post, I said I could analyze the conventional S-G experiment by standard wave theory, and if I'm so smart, why can't I do it for this one too? It looks like a fun question to work on and I have some idea how it ought to come out. So give me a day or two and let's see what I come up with...