An efficient method for solving parabolic partial differential equations is implemented in Mathematica using InterCall and an external C routine. As an application, the two-dimensional time-dependent Schroedinger's equation is solved for various initial conditions and potential functions. Four different numerical experiments are given: scattering of a particle from a cylindrical potential barrier; a double slit experiment; interaction of wave-packets; and stirring a wave-packet with a potential "stick". The resulting animations make excellant demonstrations of the properties of Schroedinger's equation. The technique used can also be applied to other similar parabolic partial differential equations.
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