  A fast and stable numerical method is formulated to compute the time
evolution of a wave function in a magnetic field by solving the time-dependent
Schroedinger equation. This computational method is based on the finite element
method in real space to improved accuracy without any increase of computational
cost. This method is also based on Suzuki's exponential product theory to
afford an efficient way to manage the TD-Schroedinger equation with a vector
potential. Applying this method to some simple electron dynamics, we have
confirmed its efficiency and accuracy.
