Fourier transform path integral method: numerical technique for scalar scattering in inhomogeneous regions

The path integral can be described as a Green´s function, although not in closed form, for Helmholtz equation in an inhomogeneous region. Here a straightforward heuristic derivation of the path integral is presented. The Fourier transform path integral method, a numerical technique applicable under scalar scattering conditions is also presented. Computational aspects of the numerical methods are discussed. Numerical examples include a source in the presence of a planar perfect electric conductor, a conducting wedge, a perfect conducting cylinder and an inhomogeneous dielectric slab