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The second edition of this book deals, as the first, with the foundations of classical physics from the 'symplectic' point of view, and of quantum mechanics from the 'metaplectic' point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the 'principle of the symplectic camel', which is a deep topological property of Hamiltonian flows. We introduce the notion of 'quantum blob', which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the 'metatron' is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.
This book deals with the foundations of classical physics from the ?symplectic? point of view, and of quantum mechanics from the ?metaplectic? point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the ?principle of the symplectic camel?, which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the ?metatron? is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation.
This book deals with the foundations of classical physics from the OC symplecticOCO point of view, and of quantum mechanics from the OC metaplecticOCO point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the OC principle of the symplectic camelOCO, which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the OC metatronOCO is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman''s integral is introduced in connection with the extended metaplectic representation. Contents: From Kepler to SchrAdinger OC and Beyond; Newtonian Mechanics; The Symplectic Group; Action and Phase; Semi-Classical Mechanics; The Metaplectic Group and the Maslov Index; SchrAdinger''s Equation and the Metatron. Readership: Researchers and graduate students in mathematical physics."
R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
"When Danah Zohar first published the early ideas of her Quantum Management Theory in the late 1990's, she articulated a new paradigm, inspired by quantum physics, and began a major contribution to our search for a new management theory that can replace outdated Taylorism. Now, in ZERO DISTANCE, the most comprehensive account of her project, she outlines how the theory has been implemented through the revolutionary RenDanHeyi business model of China's Haier Group, and subsequently several other large companies. Zohar's suggestion that the Haier model also offers a new social and political model is thought provoking. This book is a significant addition to our continuing conversation about the best way to manage companies and other human social systems. I recommend it highly." - Gary Hamel, London Business School, Author of Humanocracy This open access book offers a new management meta-theory to replace Taylorism. It presents a new paradigm in management thinking and a new, practical organizational model for implementing it in our personal and working lives, in our companies, in our communities and nations, and in a sustainable global order. It will offer an understanding of why and how "thinking-as-usual" is failing both business and political leaders in these new times, and it will advocate new thinking and new management practices that are so radically new that they turn everything we have taken for granted inside out and upside down. This new management model is called "Quantum Management Theory", because it is rooted in the new paradigm bequeathed to us by quantum physics and its younger sibling, complexity science. Danah Zohar is a physicist, philosopher, and management thought leader. She is a Visiting Professor at Tsinghua University's School of Economics and Management and a Visiting Professor at the China Academy of Art.
This is a book about the quanta that make up our universe--the highly unified bundles of energy of which everything is made. It explains wave-particle duality, randomness, quantum states, non-locality, Schrodinger's cat, quantum jumps, and more, in everyday language for non-scientists and scientists who wish to fathom science's most fundamental theory.
Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.