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?
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asked Oct 7, 2012 at 20:40
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$\begingroup$ They get split by spin... the Stern-Gerlach experiment is most commonly explained in terms of electrons (and I would be surprised if it wasn't originally carried out with electrons) $\endgroup$– Zo the RelativistOct 7, 2012 at 20:53
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$\begingroup$ @JerrySchirmer I don't think it's ever been carried out for electrons, hence the question but I could be wrong as usual ;) $\endgroup$– Larry HarsonOct 7, 2012 at 20:55
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1$\begingroup$ Jerry, you should be surprised:-) It is not feasible to do SG with electrons, since they will deflect away due to Lorentz force. $\endgroup$– Ján LalinskýJan 22, 2014 at 5:12
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$\begingroup$ But the question is, what did they expect, I heard two different answers, one said that they expected a gaussian distribution (which I doubt), the other say that they expected 3 dots, because they thought, ground state was $l=1$ state. @JánLalinský physics.stackexchange.com/q/565433/226827 $\endgroup$– sawan ktJul 13, 2020 at 6:39
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2$\begingroup$ @Shinekk Your best best bet is to find the Stern-Gerlach's paper and read what was their motivation for doing the experiment. $\endgroup$– Ján LalinskýJul 13, 2020 at 12:55
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3 Answers
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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.
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The splitting of the beam by the Stern Gerlach apparatus is one of the great myths of modern physics. The orignial experiment wasn't done with a pencil-shaped beam but with a fan-shaped beam. While it is true that the fan-shaped beam is split in two, the case of the pencil-shaped beam is quite different. I analyze it in this blog posting. The actual result for the pencil beam is a donut shape. I don't believe there is any way to get just two dots on the collection screen the way people always describe it.
answered Oct 8, 2012 at 1:09
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$\begingroup$ There is a simple way. Here're the animated results of a numerical computation of a gaussian two-dimensional spin-1/2 neutral particle in a Pauli equation, evolving in a Stern-Gerlach magnet magnetic field. If interesting, I can give the C code for generation of $\vec H$, $\psi$ and other parameters. $\endgroup$– RuslanJun 11, 2014 at 13:51
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$\begingroup$ Okay, you can get two dots if you use a numerical computation. I meant you can't get two dots if you try to do the actual experiment. $\endgroup$ Jun 11, 2014 at 16:16
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$\begingroup$ Why not? Supposedly, Pauli equation should give what experiment gives (for non-relativistic spin-1/2 particles), otherwise it doesn't work, which would be a discovery. $\endgroup$– RuslanJun 11, 2014 at 17:16
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$\begingroup$ I did, and it clearly contradicts my observations. I also did the numerical experiment with fan-shaped "beam". It shows the result of Stern-Gerlach very similar to that given in their original article. I.e. the beam splits at the center and doesn't at the borders. (I'll make a picture if you want.) Actually, if the fan is wider, then there's a splitting in another direction on its continuation. And I used the field, directly calculated for the similar magnet. Nothing in these numerical experiments supports your claims. $\endgroup$– RuslanJun 11, 2014 at 19:57
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$\begingroup$ But I didn't make any claims about the results of numerical experiments. $\endgroup$ Jun 11, 2014 at 20:29
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There is a bit of trouble with using electrons since the magnetic field of the apparatus will cause them to turn thanks to the Lorentz force. You could, of course, build a device to account for the turning, and still split the electrons by spin at the end.
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$\begingroup$ No you can't build the apparatus to do this, because the orbital splitting can't be separated from the spin-splitting, because of the degeneracies in the Dirac equation. $\endgroup$ Oct 7, 2012 at 23:30