An Error Bound for the Time-Sliced Thawed Gaussian Propagation Method

TL;DR

This paper provides a rigorous mathematical analysis and error bounds for the time-sliced thawed Gaussian propagation method used in solving the time-dependent Schrödinger equation, supported by numerical experiments.

Contribution

It introduces a triplet of operators for a formal mathematical framework and derives combined error bounds for the method's discretization and propagation steps.

Findings

Error bounds are established for the discretization and propagation processes.

Numerical experiments in 1D validate the theoretical error estimates.

Abstract

We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators to give a rigorous mathematical formulation of the method. Further, we derive combined error bounds for the discretization of the wave packet transform and the time-propagation of the thawed Gaussian basis functions. Numerical experiments in 1D illustrate the theoretical results.