= Tilted Ornstein-Uhlenbeck oscillator transformation
{title2=$\gamma_m=\kappa n^2\tau^2/2-m/\tau$}
The weighted strain density in <Ornstein-Uhlenbeck multiplicative amplification> evolves under $\mathcal L_np=(\kappa/2)p''+\tau^{-1}(\sigma p)'+n\sigma p$. Setting $p=e^{-\sigma^2/(2\kappa\tau)}\psi$ eliminates its first derivative. Shifting and scaling to $x=(\sigma-\kappa n\tau^2)/\sqrt{\kappa\tau}$ gives $\psi_{xx}+[1+\kappa n^2\tau^3-2\gamma\tau-x^2]\psi=0$. The <quantum harmonic oscillator> levels yield the displayed <eigenvalues>. Its <ground state> is the dominant positive mode; higher sign-changing modes may occur in a transient expansion.
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