Flux-normalized WKB amplitude ($E=A{k}^{-1/2}{e}^{i\int kdx}$)

For a real scalar wave equation $E^{\prime \prime }+k^{2}E=0$, the next order of the WKB approximation gives $2k{a}^{\prime }+k^{\prime }a=0$. Thus $a=A/\sqrt{k}$, and the leading Wronskian flux of a right-travelling component is $|A{|}^2$ independently of the local wavenumber.