Journal
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
Volume -, Issue -, Pages -Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2023-0094
Keywords
Pauli Equation; Operator Splitting; Time Splitting; Magnetic Schrodinger Equation; Semi-Relativistic Quantum Mechanics
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This paper analyzes a numerical method for solving the time-dependent linear Pauli equation in three dimensions. The method uses a four term operator splitting in time and proves the stability and convergence of the method. The paper also provides error estimates and meshing strategies for the case of given time-independent electromagnetic potentials, extending previous results for the magnetic Schrodinger equation.
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 Schrodinger 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 Schrodinger 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 Schrodinger equation.
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