Exact solution of Schrodinger equation for two state problem with time dependent coupling

The present work focuses on the exact solution of the time dependent Schrodinger equation involving two potentials coupled by a time dependent Dirac Delta function 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 different time variation of the strength of the Dirac Delta function potentials has been derived.