Monte Carlo Calculation of Quantum Systems. II. Higher Order Correction

Abstract

The higher order correction term is obtained for the Monte Carlo calculation of the path integral. The correction is expressed only by a modification of the potential term: \(V(\textbf{\itshape r}_{1}, \cdots , \textbf{\itshape r}_{N}) \rightarrow V+(\hbar ^{2}/24m)(\beta /M)^{2} \sum _{i=1}^{N} (\partial V/\partial \textbf{\itshape r}_{i})^{2}\), where r i 's are coordinates of particles, N is number of particles with mass m , β is ( k T ) -1 and M is number of partitions. By this method one can reduce the computation time remarkably. A rapid convergence of energy is obtained for the case of harmonic oscillator.