Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 310 / 4 / b / Solution

The exact mode functions satisfy the Wronskian normalizationUsing the Dirac delta function generated by the ladder-operator commutator therefore gives the exact canonical commutation relationThis remains true on superhorizon scales, so the exact operators do not literally commute. A claim of classical behavior must instead compare this fixed commutator with the growing statistical fluctuations, or appeal to quantum decoherence.