Quantum Mechanics with Applications to Nanotechnology and Information Science
1st Edition
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Description
Quantum mechanics transcends and supplants classical mechanics at the atomic and subatomic levels. It provides the underlying framework for many subfields of physics, chemistry and materials science, including condensed matter physics, atomic physics, molecular physics, quantum chemistry, particle physics, and nuclear physics. It is the only way we can understand the structure of materials, from the semiconductors in our computers to the metal in our automobiles. It is also the scaffolding supporting much of nanoscience and nanotechnology. The purpose of this book is to present the fundamentals of quantum theory within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology. As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today. Hence, the emphasis on new topics that are not included in older reference texts, such as quantum information theory, decoherence and dissipation, and on applications to nanotechnology, including quantum dots, wires and wells.
Key Features
- This book provides a novel approach to Quantum Mechanics whilst also giving readers the requisite background and training for the scientists and engineers of the 21st Century who need to come to grips with quantum phenomena
- The fundamentals of quantum theory are provided within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology
- Older books on quantum mechanics do not contain the amalgam of ideas, concepts and tools necessary to prepare engineers and scientists to deal with the new facets of quantum mechanics and their application to quantum information science and nanotechnology
- As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today
- There are many excellent quantum mechanics books available, but none have the emphasis on nanotechnology and quantum information science that this book has
Readership
Teaching and research faculty, upper-undergraduate and graduate students majoring in Physics, Chemistry, Chemical Engineering, Material Engineering, Electrical Engineering
Table of Contents
Preface
Acknowledgments
1. Introduction to Quantum Mechanics
1.1 What is Quantum Mechanics?
1.2 Nanotechnology and Information Technology
1.3 A First Taste of Quantum Mechanics
2. The Formalism of Quantum Mechanics
2.1 Hilbert Space and Dirac Notation
2.2 Hermitian and Anti-Hermitian Operators
2.3 The Uncertainty Principle
2.4 The Measurement Problem
2.5 Mixed States: Density Matrix Formulation
2.6 The Wigner Representation
2.7 Schrödinger and Heisenberg Representations
2.8 The Correspondence Principle and the Classical Limit
2.9 Symmetry and Conservation Laws in Quantum Mechanics
3. Angular Momentum and Spherical Symmetry
3.1 Angular Momentum in Quantum Mechanics
3.2 Spherically Symmetric Systems
3.3 Rotations and Angular Momentum
3.4 Addition (Coupling) of Angular Momenta
3.5 Tensor Operators
3.6 Symmetry Considerations
4. Spin
4.1 Spin Angular Momentum
4.2 Spinors
4.3 Electron in a Magnetic Field
4.4 Time-Reversal Properties of Spinors
4.5 Spin–Orbit Interaction in Atoms
4.6 Hyperfine Interaction
4.7 Spin-Dipolar Interactions
4.8 Introduction to Magnetic Resonance
5. Quantum Information
5.1 Classical Computation and Classical Information
5.2 Quantum Information
5.3 Quantum Computing Algorithms
5.4 Decoherence
5.5 Quantum Error Correction
5.6 Experimental Implementations
5.7 The EPR Paradox
5.8 Bell’s Inequalities
6. Quantum Dynamics and Correlations
6.1 Two-Level Systems
6.2 Three-Level Systems
6.3 Classification of Correlation and Entanglement
6.4 Three-Level System Dynamics
6.5 Continuous-Variable Systems
6.6 Wave Packet Dynamics
6.7 Time-Dependent Hamiltonians
6.8 Quantum Optimal Control Theory
7. Approximation Methods
7.1 Basis-State Expansions
7.2 Semiclassical Approximations
7.3 Perturbation Theory
7.4 Dynamics in an Electromagnetic Field
7.5 Exponential and Nonexponential Decay
7.6 The Variational Method
7.7 The Sudden Approximation
7.8 The Adiabatic Approximation
7.9 Linear Response Theory
8. Identical Particles
8.1 Permutation Symmetry
8.2 Exchange Symmetry
8.3 Permanents and Slater Determinants
8.4 Simple Two- and Three-Electron States
8.5 Exchange Symmetry for Two Two-Level Systems
8.6 Many-Particle Exchange Symmetry
9. Electronic Properties of Solids
9.1 The Free Electron Gas
9.2 Elementary Theories of Conductivity
9.3 Crystal Structure
9.4 Electrons in a Periodic Potential
9.5 Magnetic Field Effects
9.6 Semiconductors
9.7 Spintronics
9.8 Low-Energy Excitations
9.9 Insulators
10. Electronic Structure of Multielectron Systems
10.1 The Multielectron System Hamiltonian
10.2 Slater and Gaussian Type Atomic Orbitals
10.3 Term Symbols for Atoms
10.4 Two-Electron Systems
10.5 Hartree Approximation for Multielectron Systems
10.6 The Hartree–Fock Method
10.7 Koopmans’ Theorem
10.8 Atomic Radii
10.9 Multielectron Fine Structure: Hund’s Rules
10.10 Electronic Structure of Molecules
10.11 Hartree–Fock for Metals
10.12 Electron Correlation
11. Molecules
11.1 Molecular Symmetries
11.2 Diatomic Electronic States
11.3 The Born-Oppenheimer Approximation
11.4 Rotational and Vibrational Structure
11.5 Vibrational Modes and Symmetry
11.6 Selection Rules for Optical Transitions
11.7 The Franck–Condon Principle
12. Scattering Theory
12.1 Classical Scattering Theory
12.2 Quantum Scattering
12.3 Stationary Scattering Theory
12.4 Aspects of Formal Scattering Theory
12.5 Central Potentials
12.6 Resonance Scattering
12.7 Approximation Methods
12.8 Particles with Internal Degrees of Freedom
12.9 Scattering in Low-Dimensional Systems
13. Low-Dimensional Quantum Systems
13.1 Mesoscopic Systems
13.2 The Landauer Conductance Formula
13.3 Properties of Quantum Dots
13.4 Disorder in Mesoscopic Systems
13.5 Kondo Effect in Quantum Dots
13.6 Graphene
13.7 Inventory of Recently Discovered Low-Dimensional Phenomena
14. Many-Body Theory
14.1 Second Quantization
14.2 Statistical Mechanics in Second Quantization
14.3 The Electron Gas
14.4 Mean-Field Theory
15. Density Functional Theory
15.1 The Hohenberg–Kohn Theorems
15.2 The Thomas–Fermi Approximation
15.3 The Kohn–Sham Equations
15.4 Spin DFT and Magnetic Systems
15.5 The Gap Problem in DFT
15.6 Time-Dependent DFT
15.7 DFT Computer Packages
A. Linear Algebra
A.1 Vector Spaces
A.2 Operators and Matrices
B. Some Ordinary Differential Equations
C. Vector Analysis
C.1 Scalar and Vector Products
C.2 Differential Operators
C.3 Divergence and Stokes Theorems
C.4 Curvilinear Coordinates
D. Fourier Analysis
D.1 Fourier Series
D.2 Fourier Integrals
D.3 Fourier Series and Integrals in Three-Space Dimensions
D.4 Fourier Integrals of Time-Dependent Functions
D.5 Convolution
D.6 Fourier Expansion of Operators
D.7 Fourier Transforms
D.8 FT for Solving Differential and Integral Equations
E. Symmetry and Group Theory
E.1 Group Theory Axioms
E.2 Group Multiplication Tables
E.3 Examples of Groups
E.4 Some Properties of Groups
E.5 Group Representations
Bibliography
Index
Details
- No. of pages:
- 992
- Language:
- English
- Copyright:
- © Academic Press 2012
- Published:
- 27th November 2012
- Imprint:
- Academic Press
- Hardcover ISBN:
- 9780444537867
- eBook ISBN:
- 9780444537874
About the Authors
Yehuda Band
Yehuda B. Band is Professor of Chemistry, Electro-optics and Physics and a member of Ilse Katz Institute for Nanoscale Science and Technology at the Ben-Gurion University, Beer-Sheva, Israel. He holds the Snow Chair in Nanotechnology. Dr. Band has been affiliated in the past with Argonne National Laboratory, Allied-Signal Inc., National Institute for Standards and Technology (NIST), University of Chicago, Harvard-Smithsonian Center for Astrophysics and Harvard University. Dr. Band's research interests include collision theory, light scattering, nonlinear-optics electro-optics and quantum-optics, laser physics and chemistry, electronic transport properties of matter, molecular dissociation, and thermodynamics. His foremost expertise is in quantum scattering and the interaction of light with matter. He is a fellow of the American Physical Society. He is the author of about two hundred fifty scientific publications in these fields and holds numerous patents. He is the author of two books, Y. B. Band, Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers, (John Wiley, 2006), and Y. B. Band and Y. Avishai, Quantum Mechanics, with Applications to Nanotechnology and Information Science, (Elsevier, 2013). For additional information see Dr. Band’s web page, http://www.bgu.ac.il/~band
Affiliations and Expertise
Yehuda Band, Department of Chemsitry, Department of Electro-Optics and Department of Physics, and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University, Beer Sheva, Israel 84105
Yshai Avishai
Yshai Avishai is an Emeritus professor of Physics and a member of Ilse Katz Institute for Nanoscale Science and Technology at the Ben-Gurion University, Beer-Sheva, Israel. He also holds an M.A degree in Economics. After earning his Ph.D in Physics at the Weizmann institute in Rehovot, professor Avishai has been a post doctoral research associate at Argonne National Laboratory and since then he has been affiliated with the Institute de Physique Nucleaire in Lyon, the theoretical physics department and the department of condensed matter physics at Saclay, the University of Strasbourg, The University of Paris Sud at Orsay, the University of Tokyo, the University of Hokkaido, the NTT basic research laboratories and the Hong Kong University of Science and Technology. He is a fellow of the American Physical Society and contemporary Member of the Editorial Board of Physical Review Letters (Condensed matter physics). Dr. Avishai’s past research interests concentrated on the few-body problem and scattering theory in Nuclear Physics, but since 1990 they are mainly focused on theoretical condensed matter physics. These include mesoscopic systems, Anderson localization, the quantum Hall effect, quantum percolation, strongly interacting electrons and the Kondo effect and published about two hundred twenty scientific publications in these fields. Professor Avishai is the Editor of the book “Recent Progress in Many-Body Theories", (Plenum, New York, 1990), and a coauthor of two other books “Dynamical Symmetries for Nanostructures" by Konstantin Kikoin, Mikhail Kiselev and Yshai Avishai (Springer 2012) and the present book, Y. B. Band and Y. Avishai, "Quantum Mechanics, with Applications to Nanotechnology and Information Science", (Elsevier, 2013). For additional information see Dr. Avishai's web page, http://www.bgu.ac.il/~yshai
Affiliations and Expertise
Department of Physics, Ben Gurion Universitym Beer Sheva, Israel
Reviews
"...a grandiose project creating a unified source of all important information related to modern Quantum Mechanics…has a very good balance between verbal explanations and math in the text and between the text itself, problems and illustrations." --Zentralblatt MATH
"...will be of greatest interest to physics students who already have some exposure to quantum mechanics. It would work well as the textbook for a more specialized survey of topics in modern quantum physics alongside established texts dedicated to the fundamentals." --Physics Today, July 2014
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