Todd TimberlakeQuantum Chaos in the Driven Square Well

Quantum Chaos in the Driven Square Well

Overview

This website is intended to supplement an article (QuantumChaos) that has was submitted to the American Journal of Physics, but ultimately not published. The article presents several aspects of quantum chaos, or quantum dynamical behavior that is connected with chaotic motion in the classical version of the same system. The model examined is a periodically driven particle in an infinite square well. This model is simple enough to be accessible to advanced undergraduates who have taken (or are taking) an upper-level quantum mechanics course. It should also be accessible to beginning graduate students. To facilitate the use of this material in the classroom, or for student research projects, I include on this page Mathematica code that can be used to carry out many of the calculations discussed in the paper.

I later published a different paper on quantum chaos in AJP. You can find that paper, and some additional information, here.

The Mathematica Code

Below are links to a Mathematica notebook that can be used to carry out many of the calculations discussed in the paper. Along with the code is a brief description of what the code actually does. Hopefully this information, combined with the descriptions in the article, will allow anyone to use these computational tools on their own. Please feel free to use, modify, and distribute my Mathematica code as you see fit (although an attribution would be nice).

The Mathematica notebook was created using Mathematica 5.0, but it should also work in Mathematica 4.0 or later (and possibly even in earlier versions). You can read the file (without executing it) using the free MathReader software from Wolfram Research.

Etc…

For more serious computation on the driven infinite square well, my FORTRAN code (in a zip archive) is available: square. The code is documented (well, I hope) but I have not worked with this code in several years and can no longer provide assistance with implementing the programs. I hope the code can be helpful to someone as is.