Moses Fayngold, Vadim Fayngold
Quantum Mechanics and Quantum Information
Moses Fayngold graduated from the State University of Samarkand and got his PhD at the Nuclear Research Institute of Academy of Science in Uzbekistan (former USSR). He has combined teaching and research in colleges of USSR and USA, most recently as a Senior University Lectur-er at the Physics Department of the New Jersey Institute of Technology. He has lectured on Quantum Mech-anics and Special Relativity to both undergraduate and graduate students. His research interests and areas of activity include Special and General Relativity, Quantum Mechanics, Optics and optical imaging, particle scattering and propagation in peri-odic structures.
Vadim Fayngold holds two degrees M.S. in Physics and B.S. in Computer Science. While working as a research assistant at the Department of Com-puter Engineering (Polytechnic Uni-versity, New York), he focused on computer simulation of complex processes in fluid dynamics. The combined expertise he developed there has spurred his interest in the Quantum Information theory. Vadim came to the idea of writing this book while working on computer animations of various relativistic and quantum-mechanical phenomena.
Alongside a thorough definition of basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of quantum mechanics and informa-tion theory combined in one text. It deals with important topics hardly found in regular textbooks, including the Robertson-Schrdinger relation, incompatibility between angle and angular momentum, dispersed indeterminacy, interaction-free mea-surements, submissive quantum mechanics, and many others. With its in-depth discussion of key concepts complete with problems and exercises, this book is poised to become the standard textbook for advanced undergraduate and begin-ning graduate quantum mechanics courses and an essential reference for physics students and physics professionals.
From the contents:
Embryonic Quantum Mechanics: Basic Features Playing with the Amplitudes Representations and the Hilbert Space Angular Momentum Evolution of Quantum States Indeterminacy Revisited Submissive Quantum Mechanics Quantum Statistics Second Quantization Quantum Mechanics and Measurements Quantum Non-Locality Quantum Measurements and POVMs Quantum Information Quantum Gates Quantum Key Distribution
Moses Fayngold and Vadim
Quantum Mechanics andQuantum Information
Furusawa, A., van Loock, P.
Quantum Teleportation andEntanglementA Hybrid Approach to Optical QuantumInformation Processing
Coherent States in QuantumPhysics2009
Bru, D., Leuchs, G. (eds.)
Lectures on QuantumInformation2007
Audretsch, J. (ed.)
Entangled WorldThe Fascination of Quantum Informationand Computation
Stolze, J., Suter, D.
Quantum ComputingA Short Course from Theory toExperiment
Hameka, H. F.
Quantum MechanicsA Conceptual Approach
Phillips, A. C.
Introduction to QuantumMechanics2003
Quantum MechanicsConcepts and Applications
Cohen-Tannoudji, C., Diu, B., Laloe, F.
Quantum Mechanics2 Volume Set
Moses Fayngold and Vadim Fayngold
Quantum Mechanics and QuantumInformation
A Guide through the Quantum World
Moses FayngoldNJITDept. of Physi csNewark, NJ 07102-1982fayngold@mai laps.org
Vadim Fayngoldvadim.resear email@example.com
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Preface XIIIAbbreviations and Notations XIX
1 The Failure of Classical Physics 11.1 Blackbody Radiation 11.2 Heat Capacity 41.3 The Photoelectric Effect 91.4 Atoms and Their Spectra 121.5 The Double-Slit Experiment 14
Problem 19References 19
2 The First Steps into the Unknown 212.1 The BBR and Plancks Formula 212.2 Einsteins Light Quanta and BBR 242.2.1 Discussion 272.3 PEE Revisited 302.4 The Third Breakthrough: de Broglie Waves 312.4.1 Exercise 33
Problems 35References 35
3 Embryonic Quantum Mechanics: Basic Features 373.1 A Glimpse of the New Realm 373.2 Quantum-Mechanical Superposition of States 393.3 What Is Waving There (the Meaning of the C-Function)? 423.4 Observables and Their Operators 473.5 Quantum-Mechanical Indeterminacy 493.6 Indeterminacy and the World 533.7 Quantum Entanglement and Nonlocality 583.8 Quantum-Mechanical Phase Space 623.9 Determinism and Causality in Quantum World 63
3.9.1 Discussion 63Problems 66References 66
4 Playing with the Amplitudes 694.1 Composition of Amplitudes 694.2 Double Slit Revised I 744.3 Double Slit Revised II 774.4 Neutron Scattering in Crystals 784.5 Bosonic and Fermionic States 814.6 Path Integrals 89
Problems 93References 93
5 Basic Features and Mathematical Structure of QM 955.1 Observables: the Domain of Classical and Quantum
Mechanics 955.2 Quantum-Mechanical Operators 975.3 Algebra of Operators 1005.4 Eigenvalues and Eigenstates 1025.5 Orthogonality of Eigenstates 1075.6 The RobertsonSchrodinger Relation 1105.7 The Wave Function and Measurements (Discussion) 112
Problems 116References 117
6 Representations and the Hilbert Space 1196.1 Various Faces of a State Function 1196.2 Unitary Transformations 1216.3 Operators in the Matrix Form 1256.4 The Hilbert Space 1296.5 Operations in the Hilbert Space 1356.6 Nonorthogonal States 142
Problems 147References 148
7 Angular Momentum 1497.1 Orbital and Spin Angular Momenta 1497.2 The Eigenstates and Eigenvalues of L 1517.3 Operator L and Its Commutation Properties 1547.4 Spin as an Intrinsic Angular Momentum 1647.5 Angular Momentum of a Compound System 1837.6 Spherical Harmonics 188
Problems 196References 197
8 The Schrodinger Equation 1998.1 The Schrodinger Equation 1998.2 State Function and the Continuity Equation 2008.3 Separation of Temporal and Spatial Variables: Stationary
States 2038.4 The Helmholtz Equation and Dispersion Equation for a Free
Particle 2058.5 Separation of Spatial Variables and the Radial Schrodinger
Equation 2078.6 Superposition of Degenerate States 2098.7 Phase Velocity and Group Velocity 2128.8 de Broglies Waves Revised 2188.9 The Schrodinger Equation in an Arbitrary Basis 222
Problems 226References 226
9 Applications to Simple Systems: One Dimension 2279.1 A Quasi-Free Particle 2279.2 Potential Threshold 2329.3 Tunneling through a Potential Barrier 2369.4 Cold Emission 2419.5 Potential Well 2449.6 Quantum Oscillator 2499.7 Oscillator in the E-Representation 2549.8 The Origin of Energy Bands 2579.9 Periodic Structures 260
Problems 269References 271
10 Three-Dimensional Systems 27310.1 A Particle in a 3D Box 27310.2 A Free Particle in 3D (Spherical Coordinates) 27410.2.1 Discussion 27710.3 Some Properties of Solutions in Spherically Symmetric
Potential 27710.4 Spherical Potential Well 27810.5 States in the Coulomb Field and a Hydrogen Atom 28110.6 Atomic Currents 28710.7 Periodic Table 290
Problems 293References 294
11 Evolution of Quantum States 29511.1 The Time Evolution Operator 29511.2 Evolution of Operators 299
11.3 Spreading of a Gaussian Packet 30111.4 The B-Factor and Evolution of an Arbitrary State 30311.5 The Fraudulent Life of an Illegal Spike 30611.6 Jinnee Out of the Box 31111.7 Inadequacy of Nonrelativistic Approximation in Description
of Evolving Discontinuous States 31511.7.1 Discussion 31611.8 Quasi-Stationary S