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Quantum Mechanics with Applications to Nanotechnology and Information Science,

Edition 1

Editors: By Yehuda B. Band and Yshai Avishai

Publication Date: 27 Nov 2012

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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

About the author

By Yehuda B. Band, 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 and Yshai Avishai, Department of Physics, Ben Gurion Universitym Beer Sheva, Israel

PrefaceAcknowledgments1. Introduction to Quantum Mechanics1.1 What is Quantum Mechanics?1.2 Nanotechnology and Information Technology1.3 A First Taste of Quantum Mechanics2. The Formalism of Quantum Mechanics2.1 Hilbert Space and Dirac Notation2.2 Hermitian and Anti-Hermitian Operators2.3 The Uncertainty Principle2.4 The Measurement Problem2.5 Mixed States: Density Matrix Formulation2.6 The Wigner Representation2.7 Schrödinger and Heisenberg Representations2.8 The Correspondence Principle and the Classical Limit2.9 Symmetry and Conservation Laws in Quantum Mechanics3. Angular Momentum and Spherical Symmetry3.1 Angular Momentum in Quantum Mechanics3.2 Spherically Symmetric Systems3.3 Rotations and Angular Momentum3.4 Addition (Coupling) of Angular Momenta3.5 Tensor Operators 3.6 Symmetry Considerations4. Spin4.1 Spin Angular Momentum4.2 Spinors4.3 Electron in a Magnetic Field4.4 Time-Reversal Properties of Spinors4.5 Spin–Orbit Interaction in Atoms4.6 Hyperfine Interaction4.7 Spin-Dipolar Interactions4.8 Introduction to Magnetic Resonance5. Quantum Information5.1 Classical Computation and Classical Information5.2 Quantum Information5.3 Quantum Computing Algorithms5.4 Decoherence5.5 Quantum Error Correction5.6 Experimental Implementations5.7 The EPR Paradox5.8 Bell’s Inequalities6. Quantum Dynamics and Correlations6.1 Two-Level Systems6.2 Three-Level Systems6.3 Classification of Correlation and Entanglement6.4 Three-Level System Dynamics6.5 Continuous-Variable Systems6.6 Wave Packet Dynamics6.7 Time-Dependent Hamiltonians6.8 Quantum Optimal Control Theory7. Approximation Methods7.1 Basis-State Expansions7.2 Semiclassical Approximations7.3 Perturbation Theory7.4 Dynamics in an Electromagnetic Field7.5 Exponential and Nonexponential Decay7.6 The Variational Method7.7 The Sudden Approximation7.8 The Adiabatic Approximation7.9 Linear Response Theory8. Identical Particles8.1 Permutation Symmetry8.2 Exchange Symmetry8.3 Permanents and Slater Determinants8.4 Simple Two- and Three-Electron States8.5 Exchange Symmetry for Two Two-Level Systems8.6 Many-Particle Exchange Symmetry9. Electronic Properties of Solids9.1 The Free Electron Gas9.2 Elementary Theories of Conductivity9.3 Crystal Structure9.4 Electrons in a Periodic Potential9.5 Magnetic Field Effects9.6 Semiconductors9.7 Spintronics9.8 Low-Energy Excitations9.9 Insulators10. Electronic Structure of Multielectron Systems10.1 The Multielectron System Hamiltonian10.2 Slater and Gaussian Type Atomic Orbitals10.3 Term Symbols for Atoms10.4 Two-Electron Systems10.5 Hartree Approximation for Multielectron Systems10.6 The Hartree–Fock Method10.7 Koopmans’ Theorem10.8 Atomic Radii10.9 Multielectron Fine Structure: Hund’s Rules10.10 Electronic Structure of Molecules10.11 Hartree–Fock for Metals10.12 Electron Correlation11. Molecules11.1 Molecular Symmetries11.2 Diatomic Electronic States11.3 The Born-Oppenheimer Approximation11.4 Rotational and Vibrational Structure11.5 Vibrational Modes and Symmetry11.6 Selection Rules for Optical Transitions11.7 The Franck–Condon Principle12. Scattering Theory12.1 Classical Scattering Theory12.2 Quantum Scattering12.3 Stationary Scattering Theory12.4 Aspects of Formal Scattering Theory12.5 Central Potentials12.6 Resonance Scattering12.7 Approximation Methods12.8 Particles with Internal Degrees of Freedom12.9 Scattering in Low-Dimensional Systems13. Low-Dimensional Quantum Systems13.1 Mesoscopic Systems13.2 The Landauer Conductance Formula13.3 Properties of Quantum Dots13.4 Disorder in Mesoscopic Systems13.5 Kondo Effect in Quantum Dots13.6 Graphene13.7 Inventory of Recently Discovered Low-Dimensional Phenomena14. Many-Body Theory14.1 Second Quantization14.2 Statistical Mechanics in Second Quantization14.3 The Electron Gas14.4 Mean-Field Theory15. Density Functional Theory15.1 The Hohenberg–Kohn Theorems15.2 The Thomas–Fermi Approximation15.3 The Kohn–Sham Equations15.4 Spin DFT and Magnetic Systems15.5 The Gap Problem in DFT15.6 Time-Dependent DFT15.7 DFT Computer PackagesA. Linear AlgebraA.1 Vector SpacesA.2 Operators and MatricesB. Some Ordinary Differential EquationsC. Vector AnalysisC.1 Scalar and Vector ProductsC.2 Differential OperatorsC.3 Divergence and Stokes TheoremsC.4 Curvilinear CoordinatesD. Fourier AnalysisD.1 Fourier SeriesD.2 Fourier IntegralsD.3 Fourier Series and Integrals in Three-Space DimensionsD.4 Fourier Integrals of Time-Dependent FunctionsD.5 Convolution D.6 Fourier Expansion of OperatorsD.7 Fourier TransformsD.8 FT for Solving Differential and Integral EquationsE. Symmetry and Group TheoryE.1 Group Theory AxiomsE.2 Group Multiplication TablesE.3 Examples of GroupsE.4 Some Properties of GroupsE.5 Group Representations Bibliography Index

Title 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

ISBN: 9780444537867

Page Count: 992

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Teaching and research faculty, upper-undergraduate and graduate students majoring in Physics, Chemistry, Chemical Engineering, Material Engineering, Electrical Engineering

Quantum Mechanics with Applications to Nanotechnology and Information Science,

Editors: By Yehuda B. Band and Yshai Avishai

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About the author

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