Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 341 / 5 / c / Solution

The periodic centered-difference kinetic matrix $T_h$ is real symmetric, and the sampled real potential $V_h$ is a real diagonal matrix. Therefore $-i{T}_h$ and $-i{V}_h$ are skew-Hermitian, so each matrix exponential in the Strang splitting is a unitary matrix. Their product is unitary as well. Hence