A pedagogical introduction to the Schwinger variational principle: an application to low energy positron-atom scattering

We present a pedagogical introduction to the Schwinger variational principle. As a model problem, we consider the low energy positron-atom scattering in the static approximation. The mathematical aspects and physical assumptions of the method, with attention to the construction and selection of trial scattering basis sets, are discussed in detail. Emphasis is given in the numerical implementation, usually neglected in scattering textbooks where the Schwinger variational principle is presented. Issues of convergence, phase shifts, scattering lengths and elastic cross sections are presented for positron-hydrogen and positron-krypton scattering.