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 AbstractSemiclassical scattering theory can be summarized as the study ofconnections 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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