Sudden oscillator frequency quench
= Sudden oscillator frequency quench
{title2=$\alpha^2-\beta^2=1$}
A jump from <positive frequency> $\omega$ to $\Omega$ keeps an oscillator mode and its first derivative continuous. A normalized positive-frequency incident solution has outgoing coefficients $\alpha=(\Omega+\omega)/(2\sqrt{\Omega\omega})$ and $\beta=(\Omega-\omega)/(2\sqrt{\Omega\omega})$, satisfying $\alpha^2-\beta^2=1$. This temporal matching is not a sum-one spatial-scattering <probability> rule.