Zeeman Effect

Splitting of lines by orbital in a magnetic field.

$H_0+H_1=\frac{p^2}{2m}-\frac{e^2}{r}-\overrightarrow{M}\cdot \overrightarrow{B}=-\frac{{\mu }_B}{\hslash }{L}_{z}B$ Note, $[H_0,H_1]=0$, so they share an eigenbasis since $\{H,{\overrightarrow{L}}^2,L_z\}$ are a CSCO.

Split into $2\ell +1$ $m-$ levels. Thus, we have an odd number of lines.

Noticed when you see an even number of splitting lines $(2(2\ell +1))$.

Splitting of lines by spin and orbital in a magnetic field.

Hyperfine splitting?

Need $\{H,{\overrightarrow{L}}^2,L_z,{\overrightarrow{S}}^2,S_z\}$ to form a CSCO in this hyperfine splitting.