Quantum Mechanics for Beginners - with applications to quantum communication and quantum computing

Cover
Quantum Mechanics for Beginners: with applications to quantum communication and quantum computing
Copyright
Dedication
Preface
Contents
Chapter 1: What is this Book About?
	1.1 From Classical to Quantum Mechanics
	1.2 Outline of the Book
	Bibliography
Part 1: Introductory Topics
	Chapter 2: Mathematical Background
		2.1 Complex Numbers
		2.2 Trigonometry
		2.3 Vector and Scalar Quantities
		2.4 Elements of Probability Theory
		Problems
		Bibliography
	Chapter 3: Particle Dynamics
		3.1 Classical Trajectory
		3.2 Linear Momentum
		3.3 Kinetic and Potential Energy
		3.4 Inelastic and Elastic Collisions
		3.5 Angular Motion
		3.6 Angular Momentum
		3.7 Motion of an Electron in Electric and Magnetic Fields
		Problems
		Bibliography
	Chapter 4: Wave Theory
		4.1 Wave Motion
		4.2 Young’s Double-slit Experiment
		4.3 Diffraction
		4.4 Rayleigh Criterion
		Problems
		Bibliography
Part 2: Fundamentals of Quantum Mechanics
	Chapter 5: Fundamentals of Quantum Mechanics
		5.1 Quantization of Energy
		5.2 Wave–Particle Duality
		5.3 End of Certainty—Probabilistic Description
		5.4 Heisenberg Uncertainty Relations and Bohr’s Principle of Complementarity
		5.5 Coherent Superposition and Quantum Entanglement
		Problems
		Bibliography
	Chapter 6: Birth of Quantum Mechanics—Planck, Einstein, Bohr
		6.1 Brief History of Light
		6.2 Radiation Emitted by Heated Objects
		6.3 Einstein and the Photoelectric Effect
		6.4 History of the Atom till the Dawn of the Twentieth Century
		6.5 The Rutherford Atom
		6.6 The Hydrogen Spectrum
		6.7 Quantum Theory of the Atom: Bohr’s Model
		Problems
		Bibliography
	Chapter 7: De Broglie Waves: Are Electrons Waves or Particles?
		7.1 De Broglie waves
		7.2 Wave–Particle Duality—A Wavefunction Approach
		7.3 Bose–Einstein Condensation
		7.4 Heisenberg Microscope
		7.5 Compton Scattering
		Problems
		Bibliography
	Chapter 8: Quantum Interference: Wave–Particle Duality
		8.1 Young’s Double-slit Experiment for Electrons
		8.2 Einstein–Bohr Debate on Complementarity
		8.3 Delayed Choice
		8.4 Quantum Eraser
		Problems
		Bibliography
	Chapter 9: Simplest Quantum Devices: Polarizers and Beam Splitters
		9.1 Polarization of Light
		9.2 Malus’ Law for a Single Photon—Dirac’s ket–bra Notation
		9.3 Input–Output Relation for a Classical Beam Splitter
		9.4 Beam Splitter for a Single-photon State
		9.5 Polarization Beam Splitter and Pockel Cell
		Problems
		Bibliography
	Chapter 10: Quantum Superposition and Entanglement
		10.1 Coherent Superposition of States
		10.2 Quantum Entanglement and the Bell Basis
		10.3 Schrödinger’s Cat Paradox
		10.4 Quantum Teleportation
		10.5 Entanglement Swapping
		Problems
		Bibliography
	Chapter 11: No-cloning Theorem and Quantum Copying
		11.1 Cloning and Superluminal Communication
		11.2 No-cloning Theorem
		11.3 Quantum Copier
		Problems
		Bibliography
	Chapter 12: EPR and Bell Theorem
		12.1 Hidden Variables
		12.2 The Einstein–Podolsky–Rosen (EPR) Paradox
		12.3 Bohr’s Reply
		12.4 Bell’s Inequality
		12.5 Quantum Mechanical Prediction
		12.6 Experiments to Test Bell’s Inequality
		12.7 Bell–CHSH Inequality
		Problems
		Bibliography
Part 3: Quantum Communication
	Chapter 13: Quantum Secure Communication
		13.1 Binary Numbers
		13.2 Public Key Distribution, RSA
		13.3 Bennett–Brassard 84 (BB-84) Protocol
		13.4 Bennett-92 (B-92) Protocol
		13.5 Quantum Money
		Problems
		Bibliography
	Chapter 14: Optical Communication with Invisible Photons
		14.1 Mach–Zehnder Interferometer
		14.2 Interaction-free Measurement
		14.3 An Array of N Mach–Zehnder Interferometers
		14.4 Counterfactual Communication
		Problems
		Bibliography
Part 4: Quantum Computing
	Chapter 15: Quantum Computing I
		15.1 Introduction to Quantum Computing
		15.2 Quantum Logic Gates
		15.3 The Deutsch Problem
		15.4 Quantum Teleportation Revisited
		15.5 Quantum Dense Coding
		Problems
		Bibliography
	Chapter 16: Quantum Computing II
		16.1 How to Factorize N?
		16.2 Discrete Quantum Fourier Transform
		16.3 Shor’s Algorithm
		16.4 Quantum Shell Game
		16.5 Searching an Unsorted Database
		Problems
		Bibliography
Part 5: The Schrödinger Equation
	Chapter 17: The Schrödinger Equation
		17.1 The Schrödinger Equation in One Dimension
		17.2 Kinematics in Classical and Quantum Mechanics—Newton vs. Schrödinger
		17.3 Particle Inside a Box
		17.4 Tunneling Through a Barrier
		17.5 The Schrödinger Equation in Three Dimensions and the Hydrogen Atom
		Problems
		Bibliography
Index