Particle diffusion Monte Carlo (PDMC)

General expressions for anisotropic particle diffusion Monte Carlo (PDMC) in a d-dimensional space are presented. The calculations of ground state energy of a helium atom for solving the many-body Schrödinger equation is carried out by the proposed method. The accuracy and stability of the results are discussed relative to other alternative methods, and our experimental results within the statistical errors agree with the quantum Monte Carlo methods. We also clarify the benefits of the proposed method by modeling the quantum probability density of a free particle in a plane (energy eigenfunctions). The proposed model represents a remarkable improvement in terms of performance, accuracy and computational time over standard MCMC method. © 2019 Walter de Gruyter GmbH, Berlin/Boston.