Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers

Mathematical Methods and Conceptual Foundations

Guido Fano, S M Blinder (Autoren)

Buch | Softcover

XVI, 271 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-86464-8 (ISBN)

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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.

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 many-body 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 time-dependent Hartree-Fock equations, the use of non-orthogonal orbitals in Quantum Chemistry, and the asymptotic behavior of the Taylor expansion coefficients of some sequences of polynomials.

1 Twentieth Century Quantum Mechanics.- 2 Mathematical Methods in Quantum Mechanics.- 3 The Schroedinger Equation.- 4 New Adventures: Isotropic Vectors, Rotations, Spinors and Groups.- 5 Quantum Entanglement and Bell's Theorem.- 6 Digital and Quantum Computers.- Bibliography.

"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)

“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)

Erscheinungsdatum	05.03.2022
Reihe/Serie	UNITEXT for Physics
Zusatzinfo	XVI, 271 p. 142 illus., 12 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	444 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Bell’s inequality • Bell's Inequality • fundamental concepts of Quantum Mechanic for non-s • fundamental concepts of Quantum Mechanic for non-specialist • Heisenberg uncertainty principle • hidden variables • Isotropic vectors • mathematical aspects of quantum mechanics • Measurement and decoherence • Quantum Computation • Quantum Cryptography • quantum entanglement • Schrödinger equation • Spin of elementary particles
ISBN-10	3-319-86464-5 / 3319864645
ISBN-13	978-3-319-86464-8 / 9783319864648
Zustand	Neuware