The Schwinger Variational Principle: An Approach to Electron-Molecule Collisions

Abstract

In this contribution we want to discuss several features and applications of the Schwinger variational principle to the study of collisions of low energy electrons with molecules and molecular ions . The Schwinger variational principle has long been known to be a potentially useful formulation of the collision problem but until recently there have been very few applications of this variational principle to electron collision problems, The main drawback to the application of the Schwinger variational principle to more realistic systems has generally been regarded as the occurence of the term < ψ^(-)_k │V G_0 V│ ψ^(+)_k > in the variational functional. Historically this drawback seems to have outweighed the possible distinct advantages which the Schwinger variational principle is known to have over other standard variational methods such as the Kohn principle. One of these advantages results from the feature that the trial scattering wave function need not satisfy any specific asymptotic boundary conditions. This feature implies both that the trial wave function could be expanded exclusively in terms of discrete basis functions, if such expansions were advantageous in the particular problem, and that irregular functions, which must be regularized near the origin, are not required in the trial function. Moreover, the Schwinger method is not troubled by the spurious singularities that can arise in the Kohn variational method. Although various ways for avoiding the effects of these singularities in such methods have been developed it is a desirable feature of a method to be free of such singularities.

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