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 / i / Solution

Take incidence from the left and set the reactant and product potentials to zero. The asymptotic scattering boundary conditions are $\psi =A{e}^{ikx}+B{e}^{-ikx}$ for $x<0$ and $\psi =F{e}^{ikx}$ for $x>a$, with $k=\sqrt{2mE}/\hslash$. There is no incoming wave from the product side. At each finite potential step, $\psi$ and $d\psi /dx$ are continuous for the same mass on both sides.