Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / Section A / A8 / Solution

The wave numbers before and after the drop are $k=\sqrt{2mE}/\hslash$ and $q=\sqrt{2m(3E)}/\hslash =\sqrt{3}k$. Continuity of $\psi$ and ${\psi }^{\prime }$ at the finite step givesThus the reflected probability flux fraction isThe transmission probability is $(q/k)|t{|}^2=1-R$, rather than simply $|t{|}^2$. Reflection is possible at a downward potential step even though both sides are classically allowed.