= Stark effect
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An <electric field> shifts and can split the <energy eigenvalues> of an <atom (Physics)>. This is the Stark effect; its <hydrogen atom> ground-state case is quadratic in a weak field.
The observable in <Stark effect> <spectroscopy> is a change in a <spectral line>, rather than a direct reading of an individual <energy eigenvalue>. If an upper <energy eigenstate> $u$ emits a <photon> into a lower <energy eigenstate> $l$, the <Planck constant> $h$ relates its <frequency> to the difference:
$$
h\nu(\mathcal E)=E_u(\mathcal E)-E_l(\mathcal E),
\qquad
h\,\Delta\nu=\Delta E_u-\Delta E_l.
$$
Here $\mathcal E$ denotes the applied <electric field> component along a chosen axis. Both levels can move, and <electric-dipole selection rules for hydrogen> decide which pairs produce observable <spectral lines>. This makes <Stark effect> <spectroscopy> a probe of <energy eigenstates> and their <electric dipole moments>: the slope $-\partial E/\partial\mathcal E$ is the corresponding dipole component by the <Hellmann–Feynman theorem>. The comparison with <Zeeman splitting> is useful: there an applied <magnetic field> supplies the perturbation.
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