  We introduce a general class of generating functionals for the calculation of
quantum-mechanical expectation values of arbitrary functionals of fluctuating
paths with fixed end points in configuration or momentum space. The generating
functionals are calculated explicitly for harmonic oscillators with
time-dependent frequency, and used to derive a smearing formulas for
correlation functions of polynomial and nonpolynomials functions of
time-dependent positions and momenta. These formulas summarize the effect of
thermal and quantum fluctuations, and serve to derive generalized Wick rules
and Feynman diagrams for perturbation expansions of nonpolynomial interactions.
