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Animating Schroedinger's Equation in Two Dimensions

Terry Robb
Organization: RMIT University
Department: Department of Mathematics
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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.

*Science > Physics > Quantum Physics
*Wolfram Technology > Programming > Animations

applied math, physics, college courseware, graduate courseware, data analysis, tutorials, chemical engineering, communications engineering, electrical engineering, fluid chanics, mechanical engineering, nuclear engineering, graphics, animations, interfacing, intercall, mathlink, schroedinger, schroedinger's equation, partial parabolic differential equations, parabolic partial differential equations
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Schroed2D.nb (3.4 MB) - Mathematica notebook

Files specific to Mathematica 2.2 version:
Schroed2D.ma (1.7 MB) - Mathematica notebook