The present work focuses on the exact solution of the time dependent Schrodinger equation involving two potentials coupled by a Dirac Delta potential. The problem involving the partial differential equations in two variables can be reduced to a single integral equation in Laplace domain and by knowing the wave function at the origin we can derive the wave function everywhere. Solutions for the bound state and partly unbound state along with propagator are derived for the first potential. (C) 2015 Elsevier B.V. All rights reserved.