Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 324 / 3 / a / ii / Solution

For finite-dimensional matrices $A_1,\dots ,A_m$, the Lie-Trotter product formula stateswhere convergence is in operator norm. In particular, for Hermitian matrices $H_j$, set $A_j=-i{H}_j$ to obtain a product of unitary operators approximating $e^{-it{\sum }_j{H}_j}$.