Ethan's Notes

    Lamor Precession

    #Physics
    For fermions in a uniform magnetic field $\displaystyle \vec{B}=B_{0}\hat{k}$:

    $\displaystyle {\left\langle{S_{x}}\right\rangle}=-\frac{\hbar}{2}\sin \alpha \sin(\omega t)$

    • The expectation of the spin operator in the x-direction
    • $\displaystyle \alpha$ is the angle between the $\displaystyle {\left\langle{S}\right\rangle}$ and the z-axis
    • $\displaystyle \omega$ is the Lamor frequency, or frequency of precession

    $\displaystyle {\left\langle{S_{y}}\right\rangle}=-\frac{\hbar}{2}\sin \alpha \cos(\omega t)$

    $\displaystyle {\left\langle{S_{z}}\right\rangle}=\frac{\hbar}{2}\cos \alpha$