### Title page for ETD etd-08172004-122051

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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