= Spectral components of the linear hydrogen Stark effect
{c}
For an illustrative $n=2\to1s$ emission calculation, retain only the first-order shifts above and neglect the quadratic shift of the <hydrogen atom> <ground state>. The unperturbed <Lyman-alpha line> <frequency> is $\nu_0=(E_2-E_1)/h$. The possible offsets are
$$
\nu-\nu_0=-\frac{3ea_0\mathcal E}{h},\quad 0,\quad +\frac{3ea_0\mathcal E}{h}.
$$
The outer pair originates in the $p_0$ parts of $|\psi_\pm\rangle$ and has transition <electric dipole moments> along the applied <electric field>, conventionally called $\pi$ components. The central pair originates in $p_{\pm1}$ and has transverse rotating transition <electric dipole moments>, conventionally called $\sigma^\pm$ components. Because <electromagnetic radiation> is transverse, the $\pi$ components disappear when viewed along the <electric field>. Viewed from the side, the $\pi$ and $\sigma$ components have <polarization of an electromagnetic wave> respectively parallel and perpendicular to the applied <electric field>. Line intensities additionally require the initial <quantum state> populations and the collection geometry.
\Image[/stark-hydrogen-degenerate-levels.png]
{title=Linear Stark effect: a Coulomb-model prediction}
{description=Original <first excited hydrogen eigenspace> level shifts and schematic $n=2\to1s$ <spectral line> positions. Equal stick heights encode no intensities. The field scale is arbitrary. This <Lyman-alpha line> example is distinct from the visible <hydrogen> lines in the 1913 experiment.}
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