Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 34A / d / Solution

Since $[X,H]=iP$ and $⟨P⟩=\sqrt{2\omega }\Im \alpha$, the bound is
$\Delta X\Delta H\ge \sqrt{\omega /2}|\Im \alpha |$. The left side is $\sqrt{\omega /2}|\alpha |$, so equality holds exactly when $\Re \alpha =0$.

Solved by gpt-5.6-sol high.