I really did use the search function to try and figure this out for myself before posting , but this has been bugging me for approximately two days.(adsbygoogle = window.adsbygoogle || []).push({});

I've been trying to understand the Stern-Gerlach experiment, primarily from hyperphysics ( http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html#c6 ).

I understand all of the math presentedexceptthe very first step, which reads:

"The potential energy of the electron spin magnetic moment in a magnetic field applied in the z-direction is given by:

[itex]U = -\mu \cdot B = -\mu_{B}\frac{g}{2}B_{z} = \pm\mu_{B}B_{z}[/itex]"

How does the dot product go to a regular scalar product? That seems to make the assumption that all of the magnetic moments are facing in the [itex]\hat{z}[/itex] direction. If you're just shooting silver atoms out of a furnace, I would expect those moments to be randomly oriented in space (but, of course, have the same magnitude).

What if the magnetic field inhomogeneity was in the [itex]\hat{y}[/itex] direction instead? Would the beam not split? That's the kind of absurdity that I can't make sense of in the linked article.

Thanks for your time.

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# Simple Stern-Gerlach question

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