Green's Functions Associated with One and Two Dimensional Problems

In mathematics a green-s function is type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions. Green-s functions provide an important tool when we study the boundary value problem. They also have intrinsic value for a mathematician. Also green-s functions in general are distribution, not necessarily proper function. Green functions are also useful for solving wave equation, diffusion equation and in quantum mechanics, where the green-s function of the Hamiltonian is a key concept, with important links to the concept of density of states.