Theory of Electronic relaxation in solution: Exact solution in case of parabolic potential with a sink of finite width

We give a general method for finding the exact solution for the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under a potential in the presence of a sink of finite width. The solution requires the knowledge of the Green's function in Laplace domain in the absence of any sink. We find the exact solution for the case of parabolic potential. This model has considerable improvement over the existing models for understanding non-radiative electonic relaxation of a molecule in solution, in fact this is the first model where a simple analytical solution is possible in the case of a sink of finite width.