= Factorized-Hamiltonian raising trial state
{title2=$H\psi_1=-i\hbar^2f''\psi_0/m+\hbar f'\psi_1/m$}
For $Q=p-if(x)$, $H=Q^\dagger Q/(2m)$ and $Q\psi_0=0$, the trial state $\psi_1=Q^\dagger\psi_0$ obeys the displayed identity. It follows from $[Q,Q^\dagger]=2\hbar f'$ and $[p,f']=-i\hbar f''$. The coefficients are generally position-dependent multiplication functions, not constants. For linear positive $f$, the first term vanishes and the second becomes the harmonic-oscillator level spacing.
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