TwentyFirst Century Quantum Mechanics: Hilbert Space to Quantum Computers
Mathematical Methods and Conceptual Foundations
Authors: Fano, Guido, Blinder, S M
Free Preview 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
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 About this Textbook

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.
 About the authors

Guido Fano graduated magna cum laude in Physics at the University of Rome in 1955 and earned university degrees in Theoretical Physics and Mathematical Methods of Physics. He taught at several universities, including Naples, Ferrara, Bologna, and Marseille, and progressed from being an assistant lecturer to senior lecturer and, finally, Professor of Mathematical Methods of Physics. Professor Fano is a specialist in the quantum manybody problem, with particular emphasis on the mathematical aspects. He is the author of about 60 publications in international journals as well as several textbooks. He is responsible for some particularly significant results concerning the existence problem for the timedependent HartreeFock equations, the use of nonorthogonal orbitals in Quantum Chemistry, and the asymptotic behavior of the Taylor expansion coefficients of some sequences of polynomials.
Seymour M. Blinder is Professor Emeritus of Chemistry and Physics at the University of Michigan, Ann Arbor, USA. He completed his PhD at Harvard University in 1958, under the supervision of Profs. W.E. Moffitt and J.H. Van Vleck (Nobel Prize in Physics, 1977). Professor Blinder has published more than 200 publications in both Theoretical Chemistry and Mathematical Physics. He was the first to derive a closedform expression for the Feynman pathintegral propagator for the Coulomb problem (the hydrogen atom). He is the author of several books and monographs. Professor Blinder is currently a telecommuting Senior Scientist for Wolfram Research (the developers of Mathematica and other scientific software).  Reviews

“I agree with the authors that this is the excellent introductory book for nonspecialists 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)
 Table of contents (6 chapters)


TwentiethCentury Quantum Mechanics
Pages 141

Mathematical Methods in Quantum Mechanics
Pages 4384

The Schrödinger Equation
Pages 85120

New Adventures: Isotropic Vectors, Rotations, Spinors, and Groups
Pages 121151

Quantum Entanglement and Bell’s Theorem
Pages 153193

Table of contents (6 chapters)
 Download Preface 1 PDF (58.3 KB)
 Download Sample pages 2 PDF (898.6 KB)
 Download Table of contents PDF (153.9 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 TwentyFirst Century Quantum Mechanics: Hilbert Space to Quantum Computers
 Book Subtitle
 Mathematical Methods and Conceptual Foundations
 Authors

 Guido Fano
 S M Blinder
 Series Title
 UNITEXT for Physics
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG
 eBook ISBN
 9783319587325
 DOI
 10.1007/9783319587325
 Hardcover ISBN
 9783319587318
 Softcover ISBN
 9783319864648
 Series ISSN
 21987882
 Edition Number
 1
 Number of Pages
 XVI, 271
 Number of Illustrations
 130 b/w illustrations, 12 illustrations in colour
 Topics