Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation

Abstract

We propose a new algorithm for solving the semiclassical time-dependent Schrödinger equation. The algorithm is based on semiclassical wavepackets. The focus of the analysis is only on the time discretization: convergence is proved to be quadratic in the time step and linear in the semiclassical parameter $$\varepsilon$$ ε