A Path Integral Investigation and Numerical Simulation of the Two-Slit Problem in Quantum Mechanics

Abstract

In this paper we describe a complete numerical treatment of the two-slit experiment for quantum mechanics. We first introduce the two-slit problem and the Fraunhofer approximation. We describe a number of experimental approaches, including the experiment of F. Shimizu, K. Shimizu, and H. Takuma in which they subject ultracold neon atoms to the two-slit experiment. We then present the Feynman Path Integral Method and its application to the two-slit problem. Using this method, we create a toolkit to simulate this experiment, before expanding this program. We explore the visualizations created by our program, and we compare the behaviors of particles simulated in different experiments and compare the behaviors to the Fraunhofer approximation. Finally, we note how this program can then be used to simulate a variety of particles and initial conditions and their subsequent behaviors with different gratings in both the near and far regions.