  The generalized Crank-Nicolson method is employed to obtain numerical
solutions of the two-dimensional time-dependent Schrodinger equation. An
adapted alternating-direction implicit method is used, along with a high-order
finite difference scheme in space. Extra care has to be taken for the needed
precision of the time development. The method permits a systematic study of the
accuracy and efficiency in terms of powers of the spatial and temporal step
sizes. To illustrate its utility the method is applied to several
two-dimensional systems.
