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Say an isolated electron (meaning it's not part of an atom) is at rest and we turn on a homogeneous magnetic field around it. The electrons' spin undergoes the Larmor precession (except in the case where the spin was already perfectly aligned to the field). Would this precession go on infinitely in time (given the field is not turned off) or would there be a gradually loss of energy (e.g. by emission of photons) which causes the spin to more and more align with the field?

In case the precession goes on forever then what mechanism would allow the spins of electrons to align with external fields (as we know they can do)?

In case the precession fades out and the spin aligns then one would assume this happens on quite short time scales and the question arises why Larmor precession-based experiments like nuclear magnetic resonance actually work as they require the precession to be stable?

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An electron in a homogeneous magnetic field $\vec B$ has only 2 possible spin states, typically called 'spin up/down'. These two states do not refer to the total spin being perfectly aligned/anti-aligned with $\vec B$. The total quantized angular momentum is $S=\sqrt{3}/2\hbar$ while the z-component is $S_z=\pm1/2\hbar$. Thus the state of precession with $S_z$ aligned with $\vec B$ is what is generally referred to as "spin aligned". It's not the total angular momentum perfectly aligned with $\vec B$, instead it's the z-component of it. And this will precess infinitely in time. This picture answers naturally all three questions.

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