Application of the Schwinger Variational Principle for Scattering

The usual difficulty of having to evaluate double integrals with $G(x, x^{\prime })$ is avoided by considering as the trial function $U\left(x\right)=V\left(x\right)\mathrm{}\psi \mathrm{}\left(x\right)\mathrm{}$ and its Fourier transform. Numerical calculations of $s$-wave scattering by a Yukawa potential have been carried out both by means of this form of Schwinger's method and also by using Kohn's variational principle. For comparable trial functions, the latter method appears to converge faster.