# Why does Larmor precession occur in NMR?

Larmor precession is the phenomenon that in NMR the spin (and by default also the magnetic dipole moment) of protons does not line up with the applied magnetic field but rather precesses around this direction at a certain angle.

The concept of Larmor precession confuses me for several reasons:

1. The analogy is made to a children's toll which precesses in the gravitational field of the earth. And then it is claimed that since these subatomic particles spin around their axis something similar happens. BUT subatomic particles don't really spin around their axis, rather the spin is a quantum property, so how does that add up?

2. Second of all it is stated that because of their quantum nature protons can only display 2 states, ie parallel or antiparallel to the magnetic field. But if Larmor precession takes place they are no longer parallel or antiparallel?

3. The calculation of the energy of the proton in the external magnetic field comes down to:

energy= spin magnetic moment x magnetic field strength

Nowhere is there a cosine to indicate the effect of the spin magnetic moment being of axis. Surely the angle between both must matter?

• Look for the 'vector model of the atom', this is used describes the behaviour of 'spin', electrons usually, but they have the same spin properties as protons so the physics applies to them also. To answer (1) I agree that idea of fundamental particles spinning is rather odd and misleading, but the equations that describe their behaviour are similar to those for macroscopic spin, and the name stuck. (2 and 3) are answered by the vector model. Feb 6, 2020 at 19:06
• If you have a lot of protons, the component of the magnetic dipole along the axis adds up (to the bulk magnetization) and the components perpendicular will cancel out. To understand the basics of pulsed NMR, you only need to consider the bulk magnetization, see e.g. www-keeler.ch.cam.ac.uk/lectures/understanding/chapter_3.pdf
– Karsten
Feb 6, 2020 at 20:44
• @Karsten, does this mean, for the sake of argument, that when you would only have one proton in your sample there would be no Larmor precession? Feb 7, 2020 at 12:22
• @Stikke, I would suggest that you forget about about nuclei for a moment and see why a gyroscope does precession. Here is a nice illustration. The idea is derived from mechanics. mriquestions.com/why-precession.html Feb 7, 2020 at 13:41
• The quantum way to view precession that also connects to the idea of only having two quantum mechanical states is to say that when the spin is measured, you will always get aligned or anti-aligned with the field. However, the particle can actually exist in any linear combination of these two states. There will then be two time-dependent phases which correspond to states of different energies. Therefore, the average (classical) direction of the spin is neither up nor down, but at some angle to the field, where that angle is related to the energy difference of the two states. Feb 9, 2020 at 2:05