Type of Document	Dissertation
Author	Rothstein, Ivan
URN	etd-08172004-122051
Title	Semiclassical Scattering for Two and Three Body Systems
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Hagedorn, George A. Committee Chair Ball, Joseph A. Committee Member Greenberg, William Committee Member Klaus, Martin Committee Member Schmittmann, Beate Committee Member
Keywords	Semiclassical Scattering
Date of Defense	2004-08-12
Availability	unrestricted
Abstract Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit $\hbar\to 0$ over the infinite time domain $-\infty < t < \infty$. 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 $-\infty< t<\infty$. This result has long been known for dimension $n\geq 3$, 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 Schr\"{o}dinger equation for the three-body problem over the time domain $-\infty < t< \infty$. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry.
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