Quantum Mechanics with Applications to Nanotechnology and Information Science

Quantum Mechanics with Applications to Nanotechnology and Information Science

1st Edition - November 27, 2012

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  • Authors: Yehuda Band, Yshai Avishai
  • eBook ISBN: 9780444537874
  • Hardcover ISBN: 9780444537867

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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

Product details

  • No. of pages: 992
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: November 27, 2012
  • Imprint: Academic Press
  • eBook ISBN: 9780444537874
  • Hardcover ISBN: 9780444537867

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

Department of Physics, Department of Chemistry, Department of Electro-Optics, The Ilse Katz Center for Nano-Science, Ben-Gurion University of the Negev, Beer-Sheva, 8410501, Israel

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

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