Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers
Mathematical Methods and Conceptual Foundations
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Beschreibung
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.
Explains the still evolving concepts of quantum mechanics in terms accessible to nonspecialists Discusses the conceptual problems associated with measurement, superposition, and decoherence in quantum systems Examines in detail the progress toward quantum computers Includes supplementary material: sn.pub/extras
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Guido Fano
Themen in »Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers«
fundamental concepts of Quantum Mechanic for non-specialist mathematical aspects of quantum mechanics Quantum computation Heisenberg uncertainty principle Schrödinger equation Hidden variables Spin of elementary particles Isotropic vectors Quantum entanglement Bell’s inequality Measurement and decoherence Quantum cryptography
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“I agree with the authors that this is the excellent introductory book for non-specialists to quantum theory, though I would recommend it to all curious researchers whose perception of the world that surrounds us raises the questions of what, why and how is out there?” (Eugene Kryachko, zbMATH 1377.81005, 2018)
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