Document Type

Article

Journal or Conference Title

Journal of Chemical Physics

ISSN

0021-9606

Volume

95

Issue

8

First Page

5999

Last Page

6004

Publication Date

1991

Department

Natural Sciences and Mathematics

Abstract

A projection operator, similar to one previously used by us for problems with a finite set of basis functions, is suggested for use with continuous basis sets. This projection operator requires knowledge of the nodes of the density matrix at all temperatures. We show that a class of nodes, determined from the noninteracting density matrix and present at high temperatures in the interacting system are preserved to first order in the interaction at low temperatures. While we cannot show that the nodes are present at intermediate temperatures, we suspect they do exist and, as a test of this conjecture, we perform a calculation of two electrons confined in a harmonic well, using the projection operator. We find that accurate results are obtained at a range of temperatures, suggesting that our conjecture is indeed correct. We find that the error limits determined using the projection operator are 1–2 times smaller than those obtained with straightforward Monte Carlo integration (corresponding to a reduction in time of 1–4 in obtaining a desired level of accuracy).

Rights

Copyright © 1991 American Institute of Physics. All rights reserved.

Publisher Statement

Originally published as Hall, R. W., & Prince, M. R. (1991). Development, justification, and use of a projection operator in path integral calculations in continuous space. The Journal of chemical physics, 95(8), 5999-6004.

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