A time splitting method for the three-dimensional linear Pauli equation
Numerical Analysis
2023-04-05 v2 Numerical Analysis
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 Schr\"odinger 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 Schr\"odinger equation. We use a four 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 Schr\"odinger equation.
Cite
@article{arxiv.2005.06072,
title = {A time splitting method for the three-dimensional linear Pauli equation},
author = {Timon S. Gutleb and Norbert J. Mauser and Michele Ruggeri and Hans Peter Stimming},
journal= {arXiv preprint arXiv:2005.06072},
year = {2023}
}
Comments
15 pages, 3 figures