Quantum reflection probability ($R=|r{|}^2$)

For one-dimensional scattering from a real potential, write the left exterior wavefunction as $e^{ikx}+r{e}^{-ikx}$ with $k>0$. The reflected-to-incident probability-current ratio is $R=|r{|}^2$, since both components have the same speed and their currents have opposite signs. This probability differs from the complex reflection amplitude $r$. With transmission into a right exterior wavenumber $q$, the transmission probability is $T=(q/k)|t{|}^2$ and conservation of current gives $R+T=1$ when there is no absorption.