An operator-splitting fast Huygens sweeping method for Schrödinger equations with electromagnetic fields

Abstract

In this thesis, we present an operator splitting method for Schrödinger equations in the presence of electromagnetic field in the semi-classical regime. With the operator splitting technique, the time evolution of the Schrödinger equation is divided into two parts: the original Schrödinger equation and the convection step. The original Schrödinger equation can be handled by the Fast Huygens Sweeping Method(FHSM). For the convection step, we propose a semi-Lagrangian method. We show that this method performs better than the idea of the simple extension of the original FHSM. We also show that the convergence rate is nearly one because of the first order splitting error. We implement this method numerically for one dimensional, two dimensional and three dimensional cases. We also found that this method can be applied to a time-dependent vector potential.

Date of Award	2019
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology