Phase space distributions in quantum mechanics and signal analysis.
Item
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Title
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Phase space distributions in quantum mechanics and signal analysis.
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Identifier
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AAI9000041
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identifier
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9000041
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Creator
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Lee, Chongmoon.
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Contributor
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Adviser: Leon Cohen
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Date
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1989
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Atomic | Engineering, Electronics and Electrical | Physics, Acoustics
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Abstract
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We have extended the theory and applications of quasi-distributions in a number of directions. A general method for calculating the conditional expectation value of one operator for a fixed value of another has been developed. We have used this method to clarify the local virial theorem in quantum mechanics where we have shown how a phase space distribution can always be chosen so that the local virial theorem is satisfied for a particular wave function. We have also used this method to calculate the local spread of frequencies about the instantaneous frequency of a signal and obtained explicitly the expression for the instantaneous frequency and its spread for the short time energy spectrum. Having an explicit expression for the standard deviation of instantaneous frequencies allows one to calculate optimal windows for the analysis and estimation of instantaneous frequencies. Using the expression for local spread of frequencies we have been able to clarify and to find a criterion for the concept of a multicomponent signal. We have also calculated the standard deviation of the local momentum for a quantum system.;We have used a reduced density matrix approach to study certain aspects of the correlation energy problem for atomic and molecular systems. We developed an explicit model where the reduced density matrices can be calculated analytically and have applied this model to study the Colle-Salvetti method. We have shown that the Colle-Salvetti functional does not produce a N-representable reduced density matrix, however we have demonstrated why it none the less gives very accurate results for the correlation energy. In particular we have shown that it satisfies the momentum and position correlation hole very well. We have used the model problem to study the relationships between the fitting of the correlation holes and the closeness of an approximate physical quantity to the exact one.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
