# Larmor Precession - What does precession actually mean?

Larmor Precession - What does precession actually means? Is it change in the orientation of the axis with which electron revolves around the orbit? But, shouldn't the radius of the orbit remain the same?

The answer from WetSavannaAnimal is much more comprehensive (and better) than my own will be.

But just in case this helps you, I will have a go.

No offence intended, I have a feeling you might be getting the spin axis and orbital axis of the electron mixed up.

Just a quick analogy with the earth, it's tilted axis precesses, that means it describes a circle as in the illustration below. Although, obviously, the precession of the Earth's axis is much slower, it takes 26,000 years for one full circle.

If the earth was not tilted, there would be no precession, but because it is tilted, the axis of the earth moves in a circle, pointing in different directions with respect to the stars as time passes.

But the spin precession, of the earth itself, has nothing to do with the orbital motion or radius of the earth around the sun, no matter how much the axis is tilted, it will still take a year to travel around the sun.

You can apply, very roughly, the same idea to the electron but it's only an analogy and not to be taken too far.

Sorry if you know all this already, I can delete this answer if it is not applicable to you.

• +1 " I have a feeling you might be getting the spin axis and orbital axis of the election " that's a good point to make because I had this impression too now you mention it but forgot to mention it. – WetSavannaAnimal Jun 17 '15 at 11:29
• @WetSavannaAnimalakaRodVance thanks very much, I have been at this point only a year ago:) – user81619 Jun 17 '15 at 11:33

Larmor precession is the steady rotation of the direction of a magnetic moment of a particle about a magnetic field

I'm pretty sure the word is simply meant to be an analogy with the precession of a spinning rigid body's angular momentum when the body is acted on by a torque that is not aligned with the angular momentum. The reason for the analogy is that the magnetic moment of a particle is proportional to its spin angular momentum. Although we're dealing with quantum states, and the spin state resolved into the two complex $z$-direction spin-up, spin-down superposition amplitudes, there is a three-dimensional classical analogy for a large particle population all in the same quantum state. One works out the three Stokes parameters $s_j=\psi^\dagger\,\sigma_j\,\psi;\,j\in\{1,\,2,\,3\}$ where $\sigma_j$ are the Pauli spin matrices and $\psi$ is the two complex superposition amplitudes written as a $2\times 1$ column vector. It can be shown that the real, $3\times1$ column vector $\vec{X}=(s_1,\,s_2,\,s_3)$ is proportional to the magnitude and direction of a spin angular momentum measurement for the population, and it is this vector that precesses about the magnetic field $\vec{B}$ as sketched below.

Here $X$ is the Stokes vector and $B$ the magnetic induction vector. The sphere is not meant to be the particle, it is the surface of the Bloch sphere (called the Poincaré sphere when used to describe polarization in optics rather than spin states).