WKB phase correction for a slowly varying oscillator
= WKB phase correction for a slowly varying oscillator
{c}
{title2=$\sigma_1=3(K')^2/(8K^3)-K''/(4K^2)$}
For smooth $K=|k|>0$ and fixed amplitude flux, use $\sigma=K+\epsilon^2\sigma_1+\cdots$ and $A_0\propto K^{-1/2}$. The <exact amplitude-phase equation> gives $\sigma_1=A_0''/(2KA_0)$, which is the displayed formula. The first phase correction is order $\epsilon^2$ in the local wavenumber, hence order $\epsilon$ in its integrated exponential phase.