Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S3 / 1 / a

The reflection-one result describes a semi-infinite potential step, rather than a finite-width barrier. Define $k=\sqrt{2mE}/\hslash$ and $\kappa =\sqrt{2m(V_0-E)}/\hslash$. For $E>0$, takeThe growing exponential is excluded by boundedness as $x\to \infty$. Continuity of $\varphi$ and ${\varphi }^{\prime }$ at the finite step gives $1+r=c$ and $ik(1-r)=-\kappa c$, henceThe probability current of the decaying tail is zero; the reflected and incident currents have equal magnitude. This agrees with the classical reflection coefficient even though the spatial wave function differs from a classical trajectory.