# Stark Effect¶

## Stark Effect¶

The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field $\hat{H}' = e E \hat{z}$.

For a hydrogen atom in the ground state, the first-order correction to the energy vanishes.

The second-order correction is

$$\large E^2_1 \ = \ \sum_{n\neq1,l,m} \frac{|\langle nlm | e E_z | 100 \rangle |^2}{E_1 - E_n}$$