Electric-field displacement of a quantum harmonic oscillator
= Electric-field displacement of a quantum harmonic oscillator
{title2=$x_0=qE/k$}
For $H=p^2/(2m)+kx^2/2-qEx$, completing the square translates the well by $x_0=qE/k$ and shifts every <energy> by $-q^2E^2/(2k)$. The <wavefunction> of the <ground state> is translated without changing its width. Consequently the induced <electric dipole moment> is exactly linear in $E$, even when a low-order perturbative approximation to the state is inaccurate.