Faculty Sponsor: Dr. Mario Belloni
A simple problem in quantum mechanics is to analyze the scattering of a plane wave off a finite barrier. A more realistic problem is to consider the scattering of a wave packet off a finite barrier, however this problem is more difficult to solve. This research uses the solutions of the infinite square well as a basis potential for the spectral method to find the solutions to an infinite square well with different barriers added to the center of the well. We analyze the stationary states of these wells, and then construct and analyze the dynamics of a wave packet in the well incident on the barrier.