Speaker
Description
Electronic relaxation in solution is an interesting phenomenon from experimental as well as theoretical point of view. This diffusion controlled process has been theoretically modeled by using Smoluchowski equation with a position dependent sink term. The problem has been solved for different potentials and sink functions. Single state problem where Smoluchowski equation for harmonic potential with a Dirac delta sink is the most general model which has been solved analytically in Laplace domain. Due to the complexity of equation, there is no time domain solution have been reported. In this work, we will give the exact analytical solution for this problem in time domain. We have solved one dimensional Smoluchowski equation for harmonic potential with a sink of ultra-short width. This problem has been solved for single state as well as two state model exactly in time domain. We have used Green's function method to solve the equation and calculated survival probability. For two state model, survival probability for both the states have been calculated explicitly. We have developed a general method to solve single state as well as coupled two state model which can be used to solve many similar problems.
