Quantum Mechanics with Applications to Nanotechnology and Information Science.
Title:
Quantum Mechanics with Applications to Nanotechnology and Information Science.
Author:
Band, Yehuda B.
ISBN:
9780444537874
Personal Author:
Physical Description:
1 online resource (993 pages)
Contents:
Front Cover -- Quantum Mechanics: with Applications to Nanotechnology and Information Science -- Copyright -- Table of Contents -- Preface -- Acknowledgments -- 1 Introduction to Quantum Mechanics -- 1.1 What is Quantum Mechanics? -- 1.1.1 A Brief Early History of Quantum Mechanics -- 1.1.2 Energy Quantization -- 1.1.3 Waves, Light, and Blackbody Radiation -- 1.1.4 Wave-Particle Duality -- 1.1.5 Angular Momentum Quantization -- 1.1.6 Tunneling -- 1.1.7 Photoelectric Effect -- 1.2 Nanotechnology and Information Technology -- 1.2.1 STM and AFM Microscopies -- 1.2.2 Molecular Electronics -- 1.2.3 Quantum Dots, Wires and Wells, and Nanotubes -- 1.2.4 Bio-Nanotechnology -- 1.2.5 Information Technology -- 1.3 A First Taste of Quantum Mechanics -- 1.3.1 Quantum States and Probability Distributions -- 1.3.2 Observable Operators -- 1.3.3 Quantum Entanglement -- 1.3.4 The Postulates of Quantum Mechanics -- Postulates -- Wave function form of the postulates -- 1.3.5 Time-Dependent and -Independent Schrödinger Equations -- 1.3.6 Momentum, Energy, and Angular Momentum -- Generators of Galilean Transformations -- Plane Waves -- Generators of Galilean Transformations Continued -- 1.3.7 Dirac Delta Functions -- 1.3.8 Position and Momentum States,
2.2 Hermitian and Anti-Hermitian Operators -- 2.2.1 Compatible Operators and Degeneracy -- 2.3 The Uncertainty Principle -- 2.4 The Measurement Problem -- 2.5 Mixed States: Density Matrix Formulation -- 2.5.1 Many-Particle Systems: Correlation Functions -- 2.5.2 Purity and von Neumann Entropy -- 2.5.3 Distance Between States -- 2.5.4 The Measurement Problem Revisited -- 2.6 The Wigner Representation -- 2.7 Schrödinger and Heisenberg Representations -- 2.7.1 Interaction Representation -- 2.7.2 Harmonic Oscillator Raising-Lowering Operators -- 2.7.3 Coherent States and Squeezed States -- Squeezed States and the Uncertainty Principle -- 2.8 The Correspondence Principle and the Classical Limit -- 2.9 Symmetry and Conservation Laws in Quantum Mechanics -- 2.9.1 Exchange Symmetry -- 2.9.2 Inversion Symmetry -- 2.9.3 Time-Reversal Symmetry -- 2.9.4 Additional Generators of Galilean Transformations -- 3 Angular Momentum and Spherical Symmetry -- 3.1 Angular Momentum in Quantum Mechanics -- 3.1.1 Angular Momentum Raising and Lowering Operators -- 3.1.2 Electron Spin: j = 1/2 -- 3.1.3 Angular Momentum in Spherical Coordinates -- 3.1.4 Spherical Harmonics -- 3.2 Spherically Symmetric Systems -- 3.2.1 Angular Momentum Decomposition of Plane Waves -- 3.2.2 Spherical Quantum Dot -- 3.2.3 The 3D Harmonic Oscillator -- 3.2.4 The Morse Oscillator -- 3.2.5 Van der Waals and Lennard-Jones Potentials -- 3.2.6 The Hydrogen Atom -- SI, Gaussian, and Atomic Units -- The Coulomb Radial Wave Function -- The Hydrogen Atom Spectrum -- 3.3 Rotations and Angular Momentum -- 3.3.1 Euler Angles α, β, γ and the Rotation Matrix -- 3.3.2 Rotation and D Functions -- 3.3.3 Rigid-Rotor Eigenfunctions -- 3.4 Addition (Coupling) of Angular Momenta -- 3.4.1 Clebsch-Gordan Coefficients and 3j Symbols -- 3.4.2 Clebsch-Gordan Series -- 3.5 Tensor Operators.
3.5.1 Irreducible Representations of the Density Matrix -- 3.5.2 Vector Fields -- 3.5.3 Spinor Fields -- 3.5.4 Multipole Expansions -- 3.6 Symmetry Considerations -- 3.6.1 Selection Rules -- 3.6.2 Inversion Symmetry -- 3.6.3 Time-Reversal Symmetry -- 3.6.4 Wigner-Eckart Theorem -- 3.6.5 6j and Higher Coefficients -- 4 Spin -- 4.1 Spin Angular Momentum -- 4.2 Spinors -- 4.2.1 Pauli Matrices -- 4.2.2 Rotation of Spinors -- 4.2.3 Spin-Orbitals -- 4.3 Electron in a Magnetic Field -- 4.3.1 Charged Particle in a Magnetic Field: Orbital Effects -- Hydrogen Atom in a Magnetic Field: Chaos -- 4.4 Time-Reversal Properties of Spinors -- 4.5 Spin-Orbit Interaction in Atoms -- 4.6 Hyperfine Interaction -- 4.6.1 Electric Quadrupole Hyperfine Interaction -- 4.6.2 Zeeman Splitting of Hyperfine States -- 4.7 Spin-Dipolar Interactions -- 4.8 Introduction to Magnetic Resonance -- 4.8.1 The Rotating-Wave Approximation -- 4.8.2 Spin Relaxation and the Bloch Equation -- 4.8.3 Nuclear Spin Hamiltonian -- 4.8.4 Chemical Shifts -- 4.8.5 Fourier Transform NMR -- 5 Quantum Information -- 5.1 Classical Computation and Classical Information -- 5.1.1 Information and Entropy -- Information Content -- Information Source and Random Variables -- 5.1.2 Shannon Entropy -- Properties of Shannon Entropy -- 5.1.3 Data Compression -- Data Compression in Classical Information Theory -- 5.1.4 Classical Computers and Gates -- 5.1.5 Classical Cryptography -- 5.1.6 Computational Complexity -- 5.2 Quantum Information -- 5.2.1 Qubits -- 5.2.2 Quantum Entanglement and Bell States -- Entanglement Entropy -- Greenberger-Horne-Zeilinger States -- Schmidt Decomposition -- Mixed-State Entanglement -- Distillation and Dilution of Entanglement -- 5.2.3 Quantum Gates -- Single-Qubit Gates -- Two-Qubit Gates -- Three-Qubit Gates -- Quantum Gates to Make Bell States -- Universal Quantum Gates.
5.2.4 No-Cloning Theorem -- 5.2.5 Dense Coding -- 5.2.6 Data Compression of Quantum Information -- 5.2.7 Quantum Teleportation -- 5.2.8 Quantum Cryptography -- 5.2.9 Quantum Circuits -- 5.2.10 Quantum Computing Despite Measurement -- 5.3 Quantum Computing Algorithms -- 5.3.1 Deutsch and Deutsch-Jozsa Algorithms -- The Uf Gate -- The Deutsch Algorithm -- Deutsch-Jozsa Algorithm -- 5.3.2 The Grover Search Algorithm -- 5.3.3 Quantum Fourier Transform -- 5.3.4 Shor Factorization Algorithm -- Shor's algorithm: preliminaries -- Shor's Algorithm: Step by Step -- 5.3.5 Quantum Simulation -- 5.4 Decoherence -- 5.5 Quantum Error Correction -- 5.6 Experimental Implementations -- 5.6.1 Ion Traps -- 5.6.2 Neutral Atoms in Optical Lattices -- 5.6.3 Cavity Based Quantum Computing -- 5.6.4 Nuclear Magnetic Resonance Systems -- 5.6.5 All-Optical Quantum Computers -- 5.6.6 Solid-State Qubits -- Superconducting Qubits -- Quantum Dot Qubits -- 5.7 The EPR Paradox -- 5.8 Bell's Inequalities -- 5.8.1 Bell's Inequalities and the EPR Paradox -- 5.8.2 Bell's Analysis using Hidden Variables -- Relation of the Bell and CHSH Inequalities -- 5.8.3 General Aspects of Bell's Inequalities -- 6 Quantum Dynamics and Correlations -- 6.1 Two-Level Systems -- 6.1.1 Two-Level Dynamics (Spin Dynamics) -- 6.1.2 The Bloch Sphere Picture -- 6.1.3 Coupling to a Bath: Decoherence -- 6.1.4 Periodically Driven Two-Level System -- Rotating-Wave Approximation -- Adiabatic Limit -- 6.1.5 Atoms in an Electromagnetic Field: Dispersion and Absorption -- Refractive Index and Absorption -- 6.1.6 Doppler Cooling of Atoms -- 6.1.7 Optical Trapping of Atoms -- 6.1.8 Two or More Correlated "Spins" -- 6.1.9 The N-Two-Level System Bloch Sphere -- 6.1.10 Ramsey Fringe Spectroscopy -- 6.2 Three-Level Systems -- 6.2.1 Two or More Three-Level Correlated Systems.
6.3 Classification of Correlation and Entanglement -- 6.3.1 Entanglement Witness Operators -- 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 -- 7.1.1 Time-Dependent Basis Set Expansions -- 7.2 Semiclassical Approximations -- 7.2.1 The WKB Approximation -- WKB Connection Formulas -- WKB for Radial Problems -- 7.2.2 Semiclassical Treatment of Dynamics -- 7.2.3 Semiclassical Hamilton-Jacobi Expansion -- 7.3 Perturbation Theory -- 7.3.1 Nondegenerate Perturbation Theory -- Perturbative Magnetic Field Effects -- Perturbative Electric Field Effects -- 7.3.2 Degenerate Perturbation Theory -- 7.3.3 Time-Dependent Perturbation Theory -- Piecewise-Constant Perturbation -- Harmonic Perturbation -- Rotating-Wave Approximation -- Nearly Harmonic Perturbation -- 7.4 Dynamics in an Electromagnetic Field -- 7.4.1 Spontaneous and Stimulated Emission of Radiation -- 7.4.2 Electric Dipole and Multipole Radiation -- 7.4.3 Thomson, Rayleigh, Raman, and Brillouin Transitions -- 7.4.4 Decay Width -- 7.4.5 Doppler Shift -- 7.5 Exponential and Nonexponential Decay -- 7.6 The Variational Method -- 7.7 The Sudden Approximation -- 7.8 The Adiabatic Approximation -- 7.8.1 Chirped Pulse Adiabatic Passage -- 7.8.2 Stimulated Raman Adiabatic Passage -- 7.8.3 The Landau-Zener Problem -- 7.8.4 Generalized Displacements and Forces -- Generalized Forces to First Order in x(t) -- 7.8.5 Berry Phase -- 7.9 Linear Response Theory -- 7.9.1 Susceptibilities -- Translation-Invariant Media -- Kramers-Kronig Relations -- 7.9.2 Kubo Formulas -- Response to a Time-Dependent Generalized Displacement -- Generalized Conductance Matrix -- The Kubo Formula for Electrical Conductivity -- The Kubo Formula for Conductance.
7.9.3 Onsager Reciprocal Relations.
Abstract:
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. 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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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