A “canonical functions” approach to the solution of two coupled differential equations of scattering theory

The system of two coupled Schrödinger differential equations (CE) arising in the close-coupling description of electron-atom scattering is considered. A “canonical functions” approach is used. This approach replaces the integration of CE for the eigenvector with unknown initial values by the integration of CE for “canonical” functions having well-defined initial values at an arbitrary origin $r_0(0 < r_0 < \infty$). The terms of the reactance matrix are then deduced from these canonical functions. The results are independent from the choice of $r_0$. It is shown that many conventional difficulties in the numerical application are avoided, mainly that of the choice of the starting boundary variable $r_{\rm s}\sim 0$ which is automatically determined. The results of the present method are compared to those of other methods and show excellent agreement with previous accurate results