Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 30E / c / Solution

For fixed $n$, the right-hand side of the quantization equation tends to zero with $\epsilon$. Ifthe unique energy satisfies $E_n<1$, so the first branch of the action integral for a linear-to-square-root potential applies exactly. SolvinggivesThus this formula is valid whenever