A Time Splitting Method for the Three-Dimensional Linear Pauli Equation-Reference-Cited by-同舟云学术

A Time Splitting Method for the Three-Dimensional Linear Pauli Equation

Published:2023-10-06 Issue:0 Volume:0 Page:
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Gutleb Timon S.¹^ORCID,Mauser Norbert J.²,Ruggeri Michele³^ORCID,Stimming Hans Peter²

Affiliation:

1. Mathematical Institute , University of Oxford , Oxford OX2 6GG , United Kingdom

2. Research platform MMM ‘Mathematics – Magnetism – Materials’ c/o Fakultät für Mathematik , Universität Wien , A-1090 Vienna , Austria

3. Department of Mathematics and Statistics , University of Strathclyde , Glasgow G1 1XH , United Kingdom

Abstract

Abstract We analyze a numerical method to solve the time-dependent linear Pauli equation in three space dimensions. The Pauli equation is a semi-relativistic generalization of the Schrödinger equation for 2-spinors which accounts both for magnetic fields and for spin, with the latter missing in preceding numerical work on the linear magnetic Schrödinger equation. We use a four term operator splitting in time, prove stability and convergence of the method and derive error estimates as well as meshing strategies for the case of given time-independent electromagnetic potentials, thus providing a generalization of previous results for the magnetic Schrödinger equation.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2023-0094/pdf

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