Last edited 25Oct12 by bltate2@uiuc.edu
# Modeling the Schroedinger Equation

## Abstract

The focus of my project is to model simple cases of the 2 dimensional infinite rectangular well. The animations should provide a way to understand exactly how the wavefunction behaves in some of the lower energy states. The wavefunction is a tool to determine, most simply, the probabilities associated with various observations on a particle. In this case, that observation is position measurement, and the probability for a region depends on the square of the wavefunction in that region. Simulations will be available for both energy eigenstates and superpositions of such stationary states. The simulations that are of superpositions of states will evolve with time, as they should.

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## Program Screenshots

This is a screenshot of the nx=2,ny=3 energy eigenstate:

Here is the superposition of the nx=2, ny=1 and nx=4, ny=5 stationary states:

## Documentation

The simulations are split up into a separate .py files, to reduce clutter within the code and to facilitate switching between them. All of the simulations created thus far have a well with side dimensions in the ratio 1:2. Obvious improvements would include doing something about the coloration of the graphs. A second improvement that would have been nice would have been to have a second graph next to the first, with the square of the function displayed.