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

Timon S. Gutleb; Norbert J. Mauser; Michele Ruggeri; Hans Peter Stimming

doi:10.1515/cmam-2023-0094

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

Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri, Hans Peter Stimming

Mathematics And Statistics

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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 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.

Original language	English
Pages (from-to)	407-420
Number of pages	14
Journal	Computational Methods in Applied Mathematics
Volume	24
Issue number	2
Early online date	6 Oct 2023
DOIs	https://doi.org/10.1515/cmam-2023-0094
Publication status	Published - 1 Apr 2024

Funding

We acknowledge support of the Austrian Science Fund (FWF) via the grants FWF DK W1245 and SFB F65, support from the Vienna Science and Technology Fund (WWTF) project MA16-066 \u201CSEQUEX\u201D. Michele Ruggeri is a member of the \u201CGruppo Nazionale per il Calcolo Scientifico (GNCS)\u201D of the Italian \u201CIstituto Nazionale di Alta Matematica (INdAM)\u201D.

Keywords

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

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10.1515/cmam-2023-0094

Gutleb-etal-arXiv-2022-A-time-splitting-method-for-the-three-dimensional-linear-Pauli-equationSubmitted manuscript, 1.35 MBLicence: Strath_1

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title = "A time splitting method for the three-dimensional linear Pauli equation",

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AU - Gutleb, Timon S.

AU - Mauser, Norbert J.

AU - Ruggeri, Michele

AU - Stimming, Hans Peter

PY - 2024/4/1

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N2 - 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.

AB - 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.

KW - Pauli equation

KW - operator splitting

KW - time splitting

KW - magnetic Schrödinger equation

KW - semi-relativistic quantum mechanics

UR - https://doi.org/10.48550/arXiv.2005.06072

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JF - Computational Methods in Applied Mathematics

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ER -

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

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