Uncertainty of path integral averages at low temperature

Abstract

Burghardt, Eicke, and Stolze [J. Chem. Phys. 108, 1562 (1998)] have recently presented analytical results for the coherent state path integral (CSPI) approximation to the harmonic oscillator thermal density matrix in a generalized representation. In this work, the variance of the position and momentum operators for the more common Feynman path integral approximation to the density matrix is examined and compared with the results of the generalized CSPI approximation. Both path integral approaches are found to predict minimum uncertainty states at low enough temperatures. Particular attention is given to estimates of internal energy, which can place limits upon the temperature range over which path integral approximations are valid.