Editing Zeeman effect (section)

===Example: Lyman-alpha transition in hydrogen===
The [[Lyman alpha|Lyman-alpha transition]] in [[hydrogen]] in the presence of the [[spin–orbit interaction]] involves the transitions <math>2\,^2\!P_{1/2} \to 1\,^2\!S_{1/2}</math> and <math>2\,^2\!P_{3/2} \to 1\,^2\!S_{1/2}.</math>

In the presence of an external magnetic field, the weak-field Zeeman effect splits the <math>1\,^2\!S_{1/2}</math> and <math>2\,^2\!P_{1/2}</math> levels into 2 states each (<math>m_j = +1/2, -1/2</math>) and the <math>2\,^2\!P_{3/2}</math> level into 4 states (<math>m_j = +3/2, +1/2, -1/2, -3/2</math>). The Landé g-factors for the three levels are
<math display="block">\begin{align}
 g_J &= 2   & &\text{for}\ 1\,^2\!S_{1/2}\ (j = 1/2, l = 0), \\
 g_J &= 2/3 & &\text{for}\ 2\,^2\!P_{1/2}\ (j = 1/2, l = 1), \\
 g_J &= 4/3 & &\text{for}\ 2\,^2\!P_{3/2}\ (j = 3/2, l = 1).
\end{align}</math>

[[Image:Zeeman p s doublet.svg|right|300px]]
Note in particular that the size of the energy splitting is different for the different orbitals because the ''g<sub>J</sub>'' values are different. Fine-structure splitting occurs even in the absence of a magnetic field, as it is due to spin–orbit coupling. Depicted on the right is the additional Zeeman splitting, which occurs in the presence of magnetic fields.

{| class="wikitable" style="text-align:center"
|+ Dipole-allowed Lyman-alpha transitions in the weak-field regime
! Initial state<br/> <math>(n = 2, l = 1)</math><br/> <math>|j, m_j\rangle</math>
! Final state<br/> <math>(n = 1, l = 0)</math><br/> <math>|j, m_j\rangle</math>
! Energy<br/> perturbation
|-
| <math>\left| \frac{1}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\left| \frac{1}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\mp\frac{2}{3} \mu_\text{B} B</math>
|-
| <math>\left| \frac{1}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\left| \frac{1}{2}, \mp\frac{1}{2} \right\rangle</math>
| <math>\pm\frac{4}{3} \mu_\text{B} B</math>
|-
| <math>\left| \frac{3}{2}, \pm\frac{3}{2} \right\rangle</math>
| <math>\left| \frac{1}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\pm \mu_{\rm B}B </math>
|-
| <math>\left| \frac{3}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\left| \frac{1}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\mp\frac{1}{3} \mu_\text{B} B</math>
|-
| <math>\left| \frac{3}{2}, \pm\frac{1}{2} \right\rangle</math>
| <math>\left| \frac{1}{2}, \mp\frac{1}{2} \right\rangle</math>
| <math>\pm\frac{5}{3} \mu_\text{B} B</math>
|}