Zeeman Effect

Splitting of lines by orbital in a magnetic field.

\(H_0 + H_1 = \frac{p^2}{2m}-\frac{e^2}{r} - \vec{M}\cdot\vec{B}=-\frac{\mu_B}{\hbar}L_zB\) Note, \([H_0,H_1]=0\), so they share an eigenbasis since \(\{H,\vec{L}^2,L_z\}\) 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 \(\{H,\vec{L}^2,L_z,\vec{S}^2,S_z\}\) to form a CSCO in this hyperfine splitting.