 Resonant transmission through a square well

For an attractive finite square well of width $a$, outside wave number $k$ and inside wave number $q$, matching the wavefunction and its first derivative at both endpoints gives the displayed transmission probability. It equals one when $qa$ is an integer multiple of $\pi$: the internal reflections cancel. For $q=2k$ the coefficient of ${\sin }^2(qa)$ is $9/16$.