In this thesis we discuss Mori Projected Time Dynamics in a quantum mechanical system. As a precursor to calculating the time derivative of a mixed state of the system we examine the derivation of the Mori-Zwanzig formalism and different ways of calculating the time dynamics of various quantum systems. We consider the exact calculation of the time derivative of a mixed state. We then calculate the same time evolution using Mori Theory and compare the two results. From the general calculation of the Mori Equation we were able to perform a series of simple tests to compare Mori Theory to the known result. We discovered that in each of the three simple cases the Mori Equation and the direct calculation of the derivative give the same result, but in the more complicated situations the two calculations differed. This result leads us to believe that the Mori Equation is an accurate way of calculating the derivative of a mechanical variable in a quantum system.

Orientador: Bruto Max Pimentel Escobar / Banca: Miguel Alberto Manna / Banca: Diógenes Galetti / Resumo: Neste trabalho apresentamos um estudo detalhado da abordagem de Schwinger para a Mecânica Quântica, fazendo sua generalização para sistemas com escalares pertencentes ao conjunto dos quatérnions. Analisamos, em especial, a estrutura da Álgebra de Medida e sua relação com as propriedades físicas observáveis. Estudamos ainda o problema da liberdade de gauge relacionado à quantização do campo eletromagnético livre, e implementamos uma solução alternativa para este problema utilizando o Princípio Variacional de Schwinger, e o campo auxiliar B(x) introduzido por Nakanishi. / Abstract: In this work we have presented a detailed study of the Schwinger s approach to the Quantum Mechanics, making its generalization for systems with scalars which belong to the quaternion set. In particular, we have analysed the structure of the Algebra of Measurement and its relation with the observable physical properties. We have also studied the problem of the gauge freedom related to the quantization of the free electromagnetic eld and implemented an alternative solution to this one employing the Schwinger s Variational Principle and the B- eld introduced by Nakanishi. / Mestre

Thesis. 1978. B.S.--Massachusetts Institute of Technology. Dept. of Physics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / B.S.

Ng Ho Tsang = 玻色-愛因斯坦凝聚態在一個雙井形位勢的量子糾纏的理論 / 吳浩錚. / "1st November 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 159-167) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / Ng Ho Tsang = Bose-Aiyinsitan ning ju tai zai yi ge shuang jing xing wei shi de liang zi jiu chan de li lun / Wu Haozheng.

Ho Siu-wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 103-104). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Classical Information Theory --- p.2 / Chapter 1.1.1 --- Shannon Entropy --- p.3 / Chapter 1.1.2 --- "Shannon Joint Entropy, Conditional Entropy, Mutual Information and Conditional Mutual Information" --- p.5 / Chapter 1.1.3 --- Applications of Shannon Entropy --- p.7 / Chapter 1.2 --- Mathematical background for Quantum Mechanics --- p.8 / Chapter 1.2.1 --- Dirac Notation --- p.8 / Chapter 1.2.2 --- Linear Operators and Matrices --- p.11 / Chapter 1.2.3 --- Spectral Decomposition and Diagonalization --- p.11 / Chapter 1.2.4 --- Functions of Normal Matrices --- p.12 / Chapter 1.2.5 --- Trace --- p.13 / Chapter 1.2.6 --- Kronecker Product --- p.13 / Chapter 1.3 --- Elementary Quantum Mechanics --- p.14 / Chapter 1.3.1 --- State Space --- p.15 / Chapter 1.3.2 --- Evolution --- p.16 / Chapter 1.3.3 --- Quantum Measurements --- p.17 / Chapter 1.3.4 --- Joint Systems --- p.20 / Chapter 1.3.5 --- Quantum Mixtures --- p.22 / Chapter 1.3.6 --- Subsystems --- p.28 / Chapter 1.4 --- von Neumann Entropy --- p.31 / Chapter 1.4.1 --- Definition --- p.32 / Chapter 1.4.2 --- Applications of the von Neumann Entropy --- p.34 / Chapter 1.4.3 --- Conditional Entropy --- p.34 / Chapter 1.5 --- Organization of The Thesis --- p.36 / Chapter Chapter 2 --- Problem Formulations --- p.38 / Chapter 2.1 --- Measurements that Produce Pure States --- p.39 / Chapter 2.2 --- The Shannon Entropy of a Quantum States --- p.41 / Chapter 2.3 --- An Equivalent Density Matrix Obtained by Mixing Orthogonal States --- p.44 / Chapter Chapter 3 --- Pure Post-Measurement States (PPMS) Measurements --- p.46 / Chapter 3.1 --- Introduction --- p.46 / Chapter 3.2 --- Definition of PPMS measurements --- p.46 / Chapter 3.3 --- Properties of PPMS Measurement --- p.52 / Chapter 3.4 --- An Alternative Definition of von Neumann entropy in terms of PPMS Measurements --- p.73 / Chapter Chapter 4 --- Mental Measurement of a Quantum State --- p.75 / Chapter 4.1 --- Introduction --- p.75 / Chapter 4.2 --- An Alternative Definition of a Projective Measurement --- p.76 / Chapter 4.3 --- Characteristics of a Projective PPMS Measurement --- p.81 / Chapter 4.4 --- The Choice of the Mental Measurement --- p.84 / Chapter 4.5 --- An Alternative Definition of von Neumann Entropy by Means of a Mental Measurement --- p.86 / Chapter 4.6 --- Construction of the Mental Measurement --- p.86 / Chapter Chapter 5 --- Completeness of Density Matrix Postulate --- p.92 / Chapter 5.1 --- Introduction --- p.92 / Chapter 5.2 --- Complete Specification of Quantum Ensemble by Density Matrix --- p.93 / Chapter 5.3 --- An Alternative Definition of von Neumann Entropy by Shannon Entropy --- p.98 / Chapter Chapter 6 --- Conclusion and Future Works --- p.99 / Chapter 6.1 --- Conclusion --- p.99 / Chapter 6.2 --- Future Work --- p.101 / Reference --- p.103

Thèse -- Université de Paris.

Thesis (Ph. D.)--University of Michigan, 1933. / Cover title. "Reprinted from the Physical review, second series, volume 44, no. 8, October 15, 1933."

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Oregon, 2004. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 204-209). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: heterostructure; semiconductor; quantum engineering; self consistency. Includes bibliographical references (p. 30-33).