Uncertainty of path integral averages at low temperature

Burghardt, Eicke, and Stolze [J. Chem. Phys. 108, 1562 (1998)] have recentl y presented analytical results for the coherent state path integral (CSPI) approximation to the harmonic oscillator thermal density matrix in a genera lized representation. In this work, the variance of the position and moment um operators for the more common Feynman path integral approximation to the density matrix is examined and compared with the results of the generalize d CSPI approximation. Both path integral approaches are found to predict mi nimum uncertainty states at low enough temperatures. Particular attention i s given to estimates of internal energy, which can place limits upon the te mperature range over which path integral approximations are valid. (C) 2001 American Institute of Physics.