The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. The application of the Schwinger variational (SV) method to e-molecule collisions and molecular photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions. Since this is not a review of cross section data, cross sections are presented only to server as illustrative examples. In the SV method, the correct boundary condition is automatically incorporated through the use of Green's function. Thus SV calculations can employ basis functions with arbitrary boundary conditions. The iterative Schwinger method has been used extensively to study molecular photoionization. For e-molecule collisions, it is used at the static exchange level to study elastic scattering and coupled with the distorted wave approximation to study electronically inelastic scattering.