Rothstein, Ivan2014-03-142014-03-142004-08-12etd-08172004-122051http://hdl.handle.net/10919/28693Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 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 propogation of a semiclassical wavepacket 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.In CopyrightSemiclassicalScatteringDissertationhttp://scholar.lib.vt.edu/theses/available/etd-08172004-122051/