Wave turning point
= Wave turning point
{title2=$k^2(x_T)=0$}
A zero of the local squared <wavenumber> in $E''+k^2(x)E=0$. At a simple zero, $(k^2)'(x_T)\ne0$, the <WKB approximation> fails in a layer with scale $|(k^2)'(x_T)|^{-1/3}$ and the <Airy ordinary differential equation> supplies the local replacement. Two nearby <wave turning points> require a uniform treatment rather than independent <Airy turning-point connection formulas>.