Hydrogen Stark Effect

Linear splitting of the n = 2 shell under a uniform electric field

Perturbation Matrix H' = eEz

Selection rule: Δℓ = ±1, Δm = 0
Only ⟨2s|z|2p,0⟩ = −3a₀ survives.
All other matrix elements vanish.

Electric field E 0 V/m

ΔE (eV)

—

ΔE (GHz)

—

E+ (eV)

—

E− (eV)

—

Show n=1 ground state (quadratic Stark)

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Energy Level Diagram