quantum precession

Precession is the slow wobble of a spinning object's axis around another direction — the lazy circling of a leaning top instead of its falling over. In the quantum world, an angular momentum carrying a magnetic moment does much the same thing when placed in a magnetic field: its expectation-value vector swings steadily around the field axis at a fixed rate, called the Larmor frequency, set by the field strength and the particle's magnetic properties.

It helps to be careful about what is wobbling. We cannot say the angular momentum vector is literally a little arrow tracing a cone, because its perpendicular components are never sharply defined at once. What precesses cleanly is the average, the expectation value of the angular momentum, which obeys an equation almost identical to the classical one. The classical wobble survives as the motion of the quantum average — a satisfying meeting of the two pictures.

This precession is not a curiosity but a tool used every day. Nuclear magnetic resonance and the MRI scanners built on it work by tipping nuclear magnetic moments and listening to the radio signal they emit as they precess. Atomic clocks, magnetometers, and quantum-control experiments all rely on driving and reading this steady quantum wobble with exquisite precision.