= Electric dipole transition
An <electric dipole transition> is a transition driven, in the long-wavelength approximation, by the <electric-dipole interaction> $H_{\mathrm{int}}=-\mathbf d\cdot\mathbf E(t)$. Its leading amplitude is proportional to a <matrix element> of the <electric dipole moment> between the initial and final states. A vanishing element gives an <electric-dipole selection rule>; a nonzero element alone does not ensure a large probability, since the drive frequency, duration and strength also matter. For a charged <quantum harmonic oscillator> driven along its axis, $x=\sqrt{\hbar/(2m\omega)}(a+a^\dagger)$ gives the single-quantum rule $\Delta n=\pm1$.
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