Elastic scattering and the path integral

From the stationary Schrödinger equation in the framework of nonrelativistic quantum mechanics, we derive a representation of the elastic scattering amplitude in the form of a path integral. For evaluating the path integrals, we propose a method called unitary approximation. We obtain the scattering lengths and cross sections for a rectangular potential, a singular repulsive potential, and the Yukawa potential and compare with the exact results.