Lamor Precession

For fermions in a uniform magnetic field $\vec{B}=B_0\hat{k}$:

$⟨S_x⟩=-\frac{\hslash }{2}\sin \alpha \sin (\omega t)$

• The expectation of the spin operator in the x-direction
• $\alpha$ is the angle between the $⟨S⟩$ and the z-axis
• $\omega$ is the Lamor frequency, or frequency of precession

$⟨S_y⟩=-\frac{\hslash }{2}\sin \alpha \cos (\omega t)$

$⟨S_z⟩=\frac{\hslash }{2}\cos \alpha$