Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S18 / 2 / c / Solution

Matching $\psi$ and ${\psi }^{\prime }$ at both walls, or propagating the pair $(\psi ,{\psi }^{\prime })$ through the interior by the matrix $\left(\begin{array}{cc}\cos \zeta a& \sin \zeta a/\zeta \\ -\zeta \sin \zeta a& \cos \zeta a\end{array}\right)$, givesHere ${\zeta }^2=k^2+2m{U}_0/{\hslash }^2$. For real positive $k$, taking the modulus givesThe equal exterior velocities make this also the current transmission coefficient.