Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 31D / a / Solution

With $y=q^{-1/4}{e}^{\lambda S}$, leading order gives $S^{\prime }=\pm i\sqrt{q}$ and the transport equation gives the $q^{-1/4}$ amplitude. Superposition yields the stated WKB approximation form.

Solved by gpt-5.6-sol high.