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)

[thumbnail of Gutleb-etal-arXiv-2022-A-time-splitting-method-for-the-three-dimensional-linear-Pauli-equation]
Preview
Text. Filename: Gutleb_etal_arXiv_2022_A_time_splitting_method_for_the_three_dimensional_linear_Pauli_equation.pdf
Preprint
License: Strathprints license 1.0

Download (1MB)| Preview

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.