Investigation into the properties and application of the Diffusion Monte Carlo method

Abstract

This paper shall be a discussion of the properties of the Diffusion Monte Carlo (DMC) method and its applications. The discussion shall cover the basic theory behind the algorithm and the class of problems it is designed to solve: quantum systems. The algorithm will prove to be adept in producing the ground state energy and ground state wave function for systems governed by the Schrodinger equation. In this paper, familiar problems like the ground state energy of the harmonic oscillator and the Morse oscillator shall be solved using the DMC method and compared to their well-known analytic results. This will support the argument that the DMC may be used to solve problems with which the ground state energy and ground state wave function are unknown. The program outlining its use in solving these problems may be found in the accompanying appendix.