A time splitting method for the three-dimensional linear Pauli equation

Gutleb, Timon S. and Mauser, Norbert J. and Ruggeri, Michele and Stimming, Hans-Peter (2020) A time splitting method for the three-dimensional linear Pauli equation. Other. arXiv.org, Ithaca, N.Y.. (https://doi.org/10.48550/arXiv.2005.06072)

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Abstract

We present and 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, the latter missing in predeeding work on the linear magnetic Schrödinger 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 (= "linear" case), thus providing a generalization of previous results for the magnetic Schrödinger equation. Some proof of concept examples of numerical simulations are presented.

ORCID iDs

Gutleb, Timon S., Mauser, Norbert J., Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602 and Stimming, Hans-Peter;
CORE (COnnecting REpositories)