Stern-Gerlach With 3 Magnets

[LarryS]

Richard Feynman describes a “modified Stern-Gerlach” experiment in which the apparatus consists of 3 magnets in a row, along the path of the beam. The first magnet is polarity “South on top, North on bottom”. The second magnet is twice as long as the first and of opposite polarity. The third magnet is identical to the first. He then states that a beam consisting of, say, spin-one particles will be split into 3 beams when it passes the first magnet. The second magnet, being of opposite polarity will force the 3 beams back together again. And, the third magnet will continue to bring the 3 beams back together so that just one beam exists the apparatus.

Finally my question: If the third magnet is identical to the first magnet then why does it not also split the beam into 3 beams again?

Thanks in advance.

 

[The_Duck]

It's similar to this situation: I hit a baseball with my bat; now it's moving at some speed toward my partner. My partner hits it back to me twice as hard (transferring twice as much momentum), which exactly reverses its momentum. As it's coming back to me, I hit it again just as hard as I hit it originally, which brings the ball to a dead stop.

The only difference is that in the Stern-Gerlach experiment, the magnets impart different momenta to the particles depending on the particles' spin states. But whatever the spin state, this sequence of magnets will impart 0 net transverse momentum to a particle.

 

[yuiop]

This webpage http://www.upscale.utoronto.ca/PVB/Harrison/SternGerlach/SternGerlach.html has some diagrams of a Stern-Gerlach set up with 3 magnets in a row. (Go about a third of the way down the page to the section titled "Building a Spin Filter"). In that set up the beam is split into two because electrons are either spin up or spin down. I am not sure why you are talking about splitting into 3 beams, but I am not much of an expert on this so I might be missing something.

 

[Fredrik]

Finally my question: If the third magnet is identical to the first magnet then why does it not also split the beam into 3 beams again?

The first beam splits because it contains particles with different spin states. The paths of the three polarized beams will bend but not split, because particles in the same beam all have the same spin state. Also, I don't know the details, but I assume that the second magnet will have the beams going towards each other (as in the picture that yuiop posted) so none of them is parallel to the path of the original beam.

I am not sure why you are talking about splitting into 3 beams,

It must have something to do with the fact that the spin is 1 instead of the usual 1/2. (This is news to me too).

 

[yuiop]

It must have something to do with the fact that the spin is 1 instead of the usual 1/2. (This is news to me too).

That seems to be the case. A quick internet search indicates that spin 1 particles would split into 3 beams, one up, one down and one that continues in a straight line. Some examples of spin 1 particles are carbon 12 nuclei and Helium 4 atoms. (That's just general info. You probably already know that ). Nice to know we have a quick easy way to determine if something is has spin 1 or spin 1/2. Presumably a particle has to have a charge to be deflected in a Stern-Gerlach device and that is why photons are not deflected in such a device.

 

[Fredrik]

Presumably a particle has to have a charge to be deflected in a Stern-Gerlach device and that is why photons are not deflected in such a device.

What they need is a magnetic moment. The original SG experiment used silver atoms, which are of course neutral.

 

[yuiop]

What they need is a magnetic moment. The original SG experiment used silver atoms, which are of course neutral.

Thanks :)

 

[LarryS]

It's similar to this situation: I hit a baseball with my bat; now it's moving at some speed toward my partner. My partner hits it back to me twice as hard (transferring twice as much momentum), which exactly reverses its momentum. As it's coming back to me, I hit it again just as hard as I hit it originally, which brings the ball to a dead stop.

The only difference is that in the Stern-Gerlach experiment, the magnets impart different momenta to the particles depending on the particles' spin states. But whatever the spin state, this sequence of magnets will impart 0 net transverse momentum to a particle.

Great analogy. Thanks to all.