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I understand that a classical bar magnet will precess about the axis of an external magnetic field. Whilst researching NMR, I have read that nuclei with half-integer spin which are subject to an external magnetic field can occupy two possible states; spin-up and spin-down. In the spin-up state, the magnetic field generated by a nucleus is parallel to the external magnetic field, and in the spin-down state, the magnetic field generated by a nucleus is antiparallel to the external magnetic field.

Here is a diagram:

enter image description here

As you can see, the magnetic fields of the nuclei are exactly parallel or antiparallel to the external field. In my understanding, this means that they cannot precess about the external magnetic field. It seems invalid to use a model of precession in this case, yet the model is used successfully to explain NMR, what's going on?

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  • $\begingroup$ The spin-up and spin-f $\endgroup$
    – Lewis Miller
    Commented Feb 16, 2018 at 22:42
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    $\begingroup$ The spin-up and spin-down designations apply only to the components of nuclear spins in the z direction $\endgroup$
    – Lewis Miller
    Commented Feb 16, 2018 at 22:44

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The nuclei precess because they have non-zero angular momenta that make force the nuclei to resist changing their state of motion. Hence, the nuclei don't completely align with the external magnetic field, and precess instead.

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