Solution (source code)

= Solution

For $E\gg V_0$, expand the reciprocal to obtain
$$
\boxed{P(E)=1-\frac{V_0^2}{4E^2}\sin^2(\alpha a)+O[(V_0/E)^3]}.
$$
Retain the exact $\alpha$ in the bounded oscillatory factor unless a further phase expansion is controlled. Reflection is small, with an oscillatory interference correction of order $(V_0/E)^2$. The <wavefunction> is nearly a travelling wave throughout; its wave number inside is slightly smaller than outside, so its <wavelength> is slightly larger there. The reflected wave adds weak standing-wave modulation on the incident side.