Displaced quantum harmonic oscillator
= Displaced quantum harmonic oscillator
{title2=$E_n=\hbar\omega(n+1/2)-F^2/(2m\omega^2)$}
Adding $-Fx$ to the <quantum harmonic oscillator> potential gives $\frac12m\omega^2(x-d)^2-F^2/(2m\omega^2)$, where $d=F/(m\omega^2)$. Translation preserves the oscillator spectrum, apart from the displayed constant shift. Eigenfunctions are translated by $d$ and the energy spacing is unchanged.