Wronskian flux ($\mathcal{J}=\mathrm{Im}(E^{\ast }{E}^{\prime })$)

For $E^{\prime \prime }+k^2(x)E=0$ with real $k^2$, differentiation gives ${\mathcal{J}}^{\prime }=\mathrm{Im}(E^{\ast }{E}^{\prime \prime })=0$. This conserved Wronskian measures directed wave flux. In a one-dimensional ordinary plasma wave, the mean Poynting flux is $c^2\mathcal{J}/(8\pi \omega )$ in Gaussian units. It proves $R+T=1$ for a lossless two-channel scattering problem.