Solution of Multiple Scattering by Finite Iteration

We propose an iterative nonlinear solution to the general potential scattering porblem in quantum mechanics. It is illustrated by the case of $N_I$ localized scatterers of arbitrary strengths $V_j$ located at arbitrary points $R_j$ in an infinite lattice, for which we obtain the complete set of bound and scattering states. The numberical evaluation is estimated to take $O\left(N_I\right)$ steps as opposed to $O\left({N_I}^3\right)$ steps by conventional matrix inversion.