The generalized Crank-Nicolson method is employed to obtain numericalsolutions of the two-dimensional time-dependent Schrodinger equation. Anadapted alternating-direction implicit method is used, along with a high-orderfinite difference scheme in space. Extra care has to be taken for the neededprecision of the time development. The method permits a systematic study of theaccuracy and efficiency in terms of powers of the spatial and temporal stepsizes. To illustrate its utility the method is applied to severaltwo-dimensional systems.
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