Say we have an electron at rest in a uniform external magnetic field. This is a classic, simple example of a two-state system in quantum mechanics, and the mathematical analysis is pretty simple. Is there any good real-life example of this that would be nice pedagogically? For example, I would think that if you injected an unpolarized beam of electrons into a cyclotron, you would get some emission of photons (microwave?) from spin flips -- but I have no idea what the time-scale for emission would be. Maybe such an effect would be important in storage rings? Is there any simple, interesting application from outside the realm of accelerator physics? Maybe we would observe microwave radiation from free electrons in the atmosphere of the sun? Maybe effects in the earth's ionosphere?
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1$\begingroup$ Calculation of the g-factor for the magnetic dipole moment of the electron The isolated electron by Philip Ekstrom and David Wineland. It’s about Penning trap, not in the realm of accelerator physics. $\endgroup$– HolgerFiedlerCommented Nov 27, 2017 at 5:57
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$\begingroup$ @HolgerFiedler: Thanks, that's interesting. Similar to the Scientific American article, but with more detail, is Brown and Gabrielse, Rev Mod Phys 58 (1986) 233. A PDF can be found by googling. I was hoping for a simpler application or example, maybe from outside the context of a physics laboratory. It doesn't have to be an electron, could be any charged particle. It doesn't have to be a uniform field, could, e.g., be an electron in a hydrogen atom. $\endgroup$– user4552Commented Nov 27, 2017 at 16:30
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I may not fully understand what you are looking for, but MRI imaging seems like a good real-world example, or EPR spectroscopy if you prefer electrons over protons. A less well known example would be proton magnetometers.
These are all most commonly explained in terms of classically precessing magnetic moments, but in their simplest quantum mechanical essence they they are just charged fermions in an external magnetic field. The protons or electrons are spin-flipped into the higher energy quantum state by resonant microwave photons, and their spin-flip decays can be most simply observed as a microwave photon emission free induction tail. The Introduction to this undergraduate experiment discusses NMR from a simple quantum perspective.
answered Dec 28, 2017 at 16:04
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$\begingroup$ Perfect, this is exactly the kind of example I was looking for! $\endgroup$– user4552Commented Dec 28, 2017 at 21:05