THEORY OF ELECTRONIC RELAXATION IN SOLUTION - EXACT SOLUTION FOR A DELTA-FUNCTION SINK IN A PARABOLIC POTENTIAL

We give a general method for finding the exact solution for the problem of a particle undergoing diffusive motion in a potential in the presence of a delta-function sink of arbitrary position and strength. The solution requires knowledge of the Laplace transform of the Green's function for the motion in the absence of the sink. We find the exact solution for the case of the parabolic potential. This has long been an unsolved problem and is of considerable importance as a model for nonradiative electronic relaxation of a molecule in solution.