Journal of Chemical Physics
Natural Sciences and Mathematics
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).
Hall, Randall W. and Prince, Melissa R., "Development, Justification, and use of a Projection Operator in Path Integral Calculations in Continuous Space" (1991). Collected Faculty and Staff Scholarship. 198.
Copyright © 1991 American Institute of Physics. All rights reserved.
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in 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 and may be found at https://aip.scitation.org/doi/10.1063/1.461591.