A Time-Splitting for the Semiclassical Schrödinger Equation

Abstract

We propose a new algorithm for solving the semiclassical time–dependent Schr¨odinger equation. The algorithm is based on semiclassical wavepackets. Convergence is proved to be quadratic in the time step and linear in the semiclassical parameter !. To the the authors’ best knowledge, all earlier algorithms had errors that grew as the semiclassical parameter was decreased.