Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 46 / a / iv / D / Solution

For fixed $V_0$ and $a$, $0\le {\sin }^2(\alpha a)\le 1$ while the multiplier of this bounded factor tends to zero as $E^{-2}$. Consequently $\boxed{\underset{E\to \infty }{\lim }P(E)=1}$, even though the sine factor itself does not have a limit. This is the high-energy classical transmission limit.