  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.
