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Spectral and scattering theory for dispersive three-body systems
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Breeling, Michael. Spectral and scattering theory for dispersive three-body systems. Retrieved from https://doi.org/doi:10.7282/t3-4a0g-4167

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TitleSpectral and scattering theory for dispersive three-body systems
NameBreeling, Michael (author); Soffer, Avraham (chair); Goldstein, Sheldon (internal member); Kiessling, Michael (internal member); Pusateri, Fabio (outside member); Rutgers University; School of Graduate Studies
Date Created2019
Other Date2019-05 (degree)
SubjectMathematics, Quantum scattering
Extent1 online resource (vi, 78 pages)
DescriptionIn quantum scattering theory, one seeks to characterize the spectrum of and asymptotic evolution by an N-body Schrodinger Hamiltonian H. For instance, one may prove asymptotic completeness, which states that an N-body system separates into freely evolving subsystems, each of which is in a bound state.
The Mourre estimate E(H)[H,iA]E(H) > theta E(H) has been an indispensable tool in the analysis of N-body systems. It implies certain propagation estimates including local decay estimates and minimal velocity bounds. These have been used to analyze Hamiltonians p^2 + V for a broad class of N-body potentials V.
In this dissertation, we extend the Mourre theory, the subsequent propagation estimates, and the asymptotic completeness (for negative energy) to a Hamiltonian H=p^2 + |k| + V designed to capture some aspects of the photoelectric effect. Modifications are needed; the necessary inequalities are achieved by examining the spectrum and by using a different formula to compute commutators with |k|.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-4a0g-4167
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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