= Harmonic-oscillator electric polarizability
{title2=$\alpha_{\rm el}=q^2/k$}
A bound charge in a harmonic restoring potential has induced <electric dipole moment> $d=(q^2/k)E$. Completing the square proves this for every static field within the strictly harmonic model. First-order <nondegenerate perturbation theory> gives the same coefficient because the <position operator> connects the unperturbed <ground state> only to the first excited state. This exact response coefficient does not make its two-state <wavefunction> approximation exact.
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