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 / iii / Solution

Write $\psi =C{e}^{i\alpha x}+D{e}^{-i\alpha x}$ inside the barrier. Matching the wavefunction and derivative gives the four equationsFor sub-barrier energy the same equations hold by analytic continuation to imaginary $\alpha$. No coefficient solution is needed for these matching conditions.