Homework Help: Spin 1/2 particles and magnetic fields

Higgy · Apr 22, 2009

I was told that if you put a spin 1/2 particle in a magnetic field, it will align with or against the field. But some places it also says that it will precess around the field. Which one is right?

Matterwave · Apr 22, 2009

If the magnetic dipole of that particle is constant (as is in the classical case) then the dipole will allign with the magnetic field. If the magnetic dipole is proportional to the angular momentum, as is the case with actual particles \mu=\gamma*L Then the dipole (and therefore the spin) can no longer align with the magnetic field, and will precess around it (Larmer Precession).

Higgy · Apr 22, 2009

So the spin doesn't *really* align with the magnetic field, then, it just precesses around it. So what do spin 'up' and spin 'down' really refer to? To whether the magnetic moment is pointed towards the direction of the field or away from it, but not parallel or antiparallel? I guess that would make sense.

Matterwave · Apr 22, 2009

Spin up and spin down are not defined using magnetic moments. They usually mean the z-component of the spin vector (expectation) is +hbar/2 or -hbar/2 for up or down respectively.

Higgy · Apr 22, 2009

Matterwave said: ↑

Spin up and spin down are not defined using magnetic moments. They usually mean the z-component of the spin vector (expectation) is +hbar/2 or -hbar/2 for up or down respectively.

So I had it backwards? The spin is intrinsic, and the magnetic moment is defined using the spin - since spin is a type of angular momentum.

So if I put a spin 1/2 particle in a magnetic field, whether or not the spin vector points towards the field or away from it determines whether or not the magnetic dipole moment precesses towards or away from the direction of the magnetic field?

Matterwave · Apr 22, 2009

The spin is an intrinsic property of a particle (electron is 1/2, photon is 1, etc). But think of this "spin" as the "total spin". I.e. it is like the magnitude of the spin vector. The spin's "direction" and what not is determined by external "forces" and the time evolution of the spinors.

Higgy · Apr 22, 2009

Now that makes sense! (-in so much as spin is sensible) Thanks!

granpa · Apr 23, 2009

precessing particles emit radio waves until they stop precessing.
en.wikipedia.org/wiki/Magnetic_resonance_imaging