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Selected problems in time-dependent quantum mechanics
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Stucchio, Chris. Selected problems in time-dependent quantum mechanics. Retrieved from https://doi.org/doi:10.7282/T3348KQW

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Uniform TitleSelected problems in time-dependent quantum mechanics
NameStucchio, Chris (author); Soffer, Avraham (chair); Falk, Richard (internal member); Lebowitz, Joel (internal member); Costin, Ovidiu (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2008
Other Date2008-01 (degree)
SubjectMathematics, Quantum theory
Extentviii, 224 pages
DescriptionTime-dependent quantum mechanics is an important field, which is not completely understood. Of principal interest is the behavior of solutions of the time dependent Schrödinger equation, possibly including nonlinear terms to model interactions between particles.
In this work, we study the time-dependent behavior of solutions of the Schrödinger equation by a variety of methods. Using techniques of exponential asymptotics, we study the behavior of a model atom in a realistic radiation field. We prove complete ionization for such a system.
We also introduce a new method of open boundaries for numerically solving linear and nonlinear Schrodinger equations. The method introduced is the Time Dependent Phase Space Filter (TDPSF), which filters outgoing waves based on phase space localization. The method is provably correct, and can be extended to slowly decaying potentials.
NotePh.D.
NoteIncludes bibliographical references (p. 218-223).
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3348KQW
LanguageEnglish
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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