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Animating the 2-D Schroedinger equation.

• To: mathgroup at yoda.physics.unc.edu
• Subject: Animating the 2-D Schroedinger equation.
• From: TDR at vaxc.cc.monash.edu.au
• Date: 10 Mar 1993 16:55:31 +1000

Dear MathGroup,

 A week or so ago I said I'd post a Notebook to MathSource on how
to generate some animations of the one-dimensional time-dependent
Schroedinger equation. This I did last week, although I haven't
received an acknowledgement yet, so it could be a few more days
before it is obtainable from there.

As a bonus I've also produced another Notebook that can numerically
solve the TWO-dimensional time-dependent Schroedinger equation, and
I have posted it to MathSource too.

The new Notebook contains some wonderful density-plot animations.

With the Notebook, various interactive experiments can done and the
probability field gets displayed as a density plot. In one experiment
I took a wave-packet (a fuzzy blob in one corner) that moves across
the screen to get scattered off a potential column -- it's a very neat
animation that illustrates what a symbolic/numeric interface such as
InterCall can achieve. By using the InterCall package I was able to
write the potential function in Mathematica and yet pass it as an
argument to a parabolic partial differential equation solver within
in C. This made interactive experiments very easy and also fast.

Here is the abstract for the new Notebook that I have sent to
MathSource -- I hope someone at wri will put the Notebook in
the MathSource directory soon ;-)

++++++++++++++++++++
Animating Schroedinger's equation in two-dimensions.

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 off
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.
Also the technique used can be applied to other similar
parabolic partial differential equations.
++++++++++++++++++++

Terry.