PATH INTEGRATION OF A GENERAL 2 TIME ACTION INVOLVING LOCAL AND NONLOCAL HARMONIC-OSCILLATOR POTENTIALS

Path integration of a general two-time quadratic action having local a nd nonlocal harmonic oscillator potentials is performed within the fra mework of Feynman's polygonal path approach. The propagator (or the de nsity matrix) thus obtained is diagonalized and the values of energies and eigenfunctions of a large number of states as a function of the s trength of the nonlocal potential which simulates the effect of the me dium on the solute represented by the local harmonic oscillator potent ial are derived. These values are used to calculate the effect of the solvent on the various properties of the solute. The possibility of re presenting the propagator in terms of an effective local action is als o explored.