Convergence of the Sasakawa Expansion for the Scattering Amplitude

Sasakawa has rewritten Schrödinger's integral equation in such a manner that the inhomogeneous term has the asymptotic behavior of the exact scattering wave function. This paper gives a proof that the iterative solution for the scattering amplitude converges for all local potentials for which the function $\mathrm{rV}\left(r\right)\mathrm{}$ is absolutely integrable. Under very general conditions the kernel of the Sasakawa equation is a Hilbert-Schmidt kernel. The integral equation is convenient for numerical solution in both the radial representation and the momentum representation.