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 (2024) A time splitting method for the three-dimensional linear Pauli equation. Computational Methods in Applied Mathematics, 24 (2). pp. 407-420. ISSN 1609-9389 (https://doi.org/10.1515/cmam-2023-0094)

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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.