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Selected problems in time-dependent quantum mechanics
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Title
Selected problems in time-dependent quantum mechanics
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Stucchio
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Chris
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Chris Stucchio
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author
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Soffer
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Avraham
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Advisory Committee
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Avraham Soffer
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chair
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Falk
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Richard
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Richard Falk
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internal member
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Lebowitz
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Joel
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Joel Lebowitz
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Costin
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Ovidiu
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Advisory Committee
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Ovidiu Costin
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Rutgers University
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Graduate School - New Brunswick
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theses
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2008
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2008-01
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English
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electronic
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viii, 224 pages
Abstract
Time-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.
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.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 218-223).
Subject
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Topic
Mathematics
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Topic
Quantum theory
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17224
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ETD_601
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Identifier
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doi:10.7282/T3348KQW
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ETD doctoral
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Copyright protected
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Open
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Chris Stucchio
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Rutgers University. Graduate School - New Brunswick
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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