Application of the Feynman-Kac path integral method in finding the ground state of quantum systems

Abstract

Numerical methods of applying the Feynman-Kac path integral approach to quantum mechanics are presented. The methods are demonstrated on simple quantum mechanical systems, including the hydrogen atom, the simple harmonic oscillator and infinite square wells. New analytic results for the Wiener integrals are obtained and compared with numerical results. A measure of the statistical uncertainty is introduced and rates of convergence are investigated. Implementation of the method on both serial and parallel computers is discussed. © 1997 Elsevier Science B.V.