Semiclassical Scattering for Two and Three Body System

Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ~ → 0 over the infinite time domain − ∞ < t < ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propagation of a semiclassical wave-packet over the time domain − ∞ < t <∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain − ∞ < t < ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry. Contents