Does the spin precession change sign when the angular momentum does? Say you have a charged particle moving circularly in an electromagnetic field. Basic quantum mechanics tell us that its spin will precess with a certain frequency. If the same particle were traveling circularly in the opposite direction (e.g. clockwise instead of counterclockwise or vice versa) would the spin precess in the opposite direction as well, or would it stay the same?
EDIT: I'm assuming that in the second case, it's traveling in the opposite direction in the same field. This may mean that the field has the be purely electric, and not magnetic, for this scenario to be possible.
EDIT 2: If the field is purely electric, then classically the spin shouldn't precess at all. However, in the special relativistic case, the electric and magnetic fields are part of one tensor, and they both affect the precession. So if you're looking at this using a quantum mechanical Hamiltonian you may want to keep this in mind and use the Dirac equation instead of the Schrodinger equation.
 A: If a charged particle is moving along a circle, then it is moving in a pure magnetic field. An electric field would be accelerating it in a particular direction.
The magnetic field $\vec B$ causes the spin-up and spin-down state rotate their quantum phases at different rates, because of the energy difference $-\vec B\cdot \Delta\vec \mu$ where $\vec\mu\sim \vec S$ is the magnetic moment proportional to the spin.
If the direction of the circle changes from clockwise to counter-clockwise, it indeed means that $\vec B$ had to change the sign, too. If it does, the difference between the rates of the spin-up and spin-down wave function changes, and the precession therefore proceeds in the opposite direction, too (assuming that the average component of the spin in the direction of the magnetic field – I mean in an axis whose direction we keep fix and don't reflect when $\vec B$ flips the sign – is conserved during the re-polarization of $\vec B$).
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