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

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.