  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.
