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

Lucchese, R. R. and Takatsuka, K. and Watson, D. K. and McKoy, V. (1983) The Schwinger Variational Principle: An Approach to Electron-Molecule Collisions. In: Electron-Atom and Electron-Molecule Collisions. Physics of Atoms and Molecules. Springer , pp. 29-49. ISBN 978-1-4899-2150-5.

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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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Additional Information:© 1983 Springer. This work was supported by grant No. CHE79-15807 from the National Science Foundation and by an Institutional grant from the United States Department of Energy No. EY-76-G-03- 1305. The research reported in this paper made use of the Dreyfus-NSF Theoretical Chemistry Computer which was funded through grants from the Camille and Henry Dreyfus Foundation, the National Science Foundation (Grant No. CHE78-20235), and the Sloan Fund of the California Institute of Technology.
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Department of Energy (DOE)EY-76-G-03- 1305
Camille and Henry Dreyfus FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Series Name:Physics of Atoms and Molecules
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ID Code:62216
Deposited On:19 Nov 2015 20:33
Last Modified:10 Nov 2021 22:59

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