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 Schr\"odinger 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 Schr\"odinger 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, thus providing a generalization of previous results for the magnetic Schr\"odinger equation.

翻译：我们分析了一种数值方法，用于求解三维空间中的含时线性Pauli方程。Pauli方程是描述2-旋量的薛定谔方程的半相对论推广，同时考虑了磁场和自旋效应，而自旋在先前关于线性磁薛定谔方程的数值工作中是缺失的。我们采用时间四算子分裂方法，证明了该方法的稳定性和收敛性，推导了误差估计，并针对给定的时不变电磁势情形给出了网格划分策略，从而推广了先前关于磁薛定谔方程的研究结果。