T. S. Gutleb, N. Mauser, M. Ruggeri, H. P. Stimming:

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

in: "ASC Report 15/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 21.

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.

Pauli equation, operator splitting, time splitting, magnetic Schrödinger equation, semi-relativistic quantum mechanics

http://www.asc.tuwien.ac.at/preprint/2020/asc15x2020.pdf

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