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# Quantum Mechanics with Applications to Nanotechnology and Information Science

- 1st Edition - November 27, 2012
- Authors: Yehuda B. Band, Yshai Avishai
- Language: English
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 5 3 7 8 6 - 7
- eBook ISBN:9 7 8 - 0 - 4 4 4 - 5 3 7 8 7 - 4

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… Read more

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Request a sales quoteQuantum 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.

- 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

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

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

- No. of pages: 992
- Language: English
- Edition: 1
- Published: November 27, 2012
- Imprint: Academic Press
- Hardback ISBN: 9780444537867
- eBook ISBN: 9780444537874

YB

### Yehuda B. 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, IsraelYA

### 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, IsraelRead

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