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A Study into Quantum Scattering with a Hard Sphere Potential
Abstract: Most of our current knowledge about fundamental interactions comes from particle scattering experiments. In these experiments, a beam of projectiles is prepared in a well-defined initial state and is sent towards a target region. Interactions with the target cause the incoming projectiles to scatter in different directions due to the type of interaction that takes place in the target region. We present a study into the scattering between a particle and an infinite sphere potential, comparing theoretical results with those found using various numerical techniques. The wave function of the particle was found using the numerov method, and was in turn used to calculate the phase shifts of the wave function for different angular momentum values. Using the phase shifts, a partial wave analysis was conducted in order to find the differential and total cross sections of the interaction for different deflection angles and energies. Our results show strong agreement between theoretically accepted and numerical values for the phase shifts and differential and total cross sections of the scattering event. This agreement shows the utility of the numerov method for solving the Schrödinger equation with one-dimensional potentials, and the advantage of using partial wave analysis to study wave functions.
Faculty Advisor: Dr. Jay Wang