Numerical errors resulting from finite-difference approximation in computations of a one-dimensional Schrödinger equation with the Trotter formula

The parallel algorithm for solving time-dependent Schrödinger equations devised by De Raedt and based on the Trotter formula is not only simple but also unconditionally stable, explicit, and local. We consider the numerical errors resulting from the finite-difference approximation of De Raedt's algorithm by comparing an exact solution of a free particle with the approximate solution calculated by using the Trotter formula, which depends on the size of the spatial-temporal lattice.