三维线性泡利方程的时间分裂方法

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-10-06 DOI:10.1515/cmam-2023-0094

Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri, Hans Peter Stimming

{"title":"三维线性泡利方程的时间分裂方法","authors":"Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri, Hans Peter Stimming","doi":"10.1515/cmam-2023-0094","DOIUrl":null,"url":null,"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.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"100 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Time Splitting Method for the Three-Dimensional Linear Pauli Equation\",\"authors\":\"Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri, Hans Peter Stimming\",\"doi\":\"10.1515/cmam-2023-0094\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":48751,\"journal\":{\"name\":\"Computational Methods in Applied Mathematics\",\"volume\":\"100 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-10-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/cmam-2023-0094\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/cmam-2023-0094","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要分析了三维空间中时变线性泡利方程的数值求解方法。泡利方程是对2旋量Schrödinger方程的半相对论推广，该方程考虑了磁场和自旋，而后者在之前对线性磁Schrödinger方程的数值工作中缺失。我们使用四项算子在时间上分裂，证明了该方法的稳定性和收敛性，并推导了给定时无关电磁势情况下的误差估计和网格划分策略，从而为磁性Schrödinger方程的先前结果提供了推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.