Concluding Remarks

Abstract

This monograph represents a study of a class of semiclassical methods for analysing atomic and molecular scattering which appears more systematic than some ad hoc approximation methods often termed semiclassical. The latter are, in fact, quite wide ranging. The subjects chosen reflect the author’s past work and attitude towards approximations in molecular scattering theory. Our scientific tastes are varied, and one man’s delight may turn out to be another’s indifference. In any event, despite the enhanced accuracy experimental techniques have achieved, approximation methods are not only useful and practical, but also a necessity, although immense progress has been made in numerical methods with the help of digital computers. Judicious combination of approximations and numerical methods appears to hold out promise, and an important point of the present work is in advocating that notion towards collision problems. As shown with some examples, the WKB method, when treated correctly, is probably the most powerful and accurate among various approximation methods at the lowest level of approximation. Since systematic approximation schemes are not realizable divorced from some observance of mathematical rigor, attempts have been made to preserve the rigor wherever possible and practicable.