Quantum mechanics is a highly successful yet mysterious theory. Quantum Mechanics for Beginners provides an accessible introduction to this fascinating subject for those with only a high school background in physics and mathematics. This book is entirely algebra-based, except for the last chapter on the Schrodinger equation. A major advantage of this book is that it provides an introduction to the fields of quantum communication and quantum computing.
Topics covered include wave-particle duality, Heisenberg uncertainty relation, Bohr's principle of complementarity, quantum superposition and entanglement, Schrodinger's cat, Einstein-Podolsky-Rosen paradox, Bell theorem, quantum no-cloning theorem and quantum copying, quantum eraser and delayed choice, quantum teleportation, quantum key distribution protocols such as BB-84 and B-92, counterfactual communication, quantum money, quantum Fourier transform, quantum computing protocols including Shor and Grover algorithms, quantum dense coding, and quantum tunneling. All these topics and more are explained fully, but using only elementary mathematics. Each chapter is followed by exercises and a short list of references.
This book is meant for beginning college students as well as advanced high school students, and can be used as a text for a one-semester course at the undergraduate level. It can also be useful for those who want to learn some of the fascinating recent and ongoing developments in areas related to the foundations of quantum mechanics and its applications to areas like quantum communication and quantum computing.
Author(s): M. Suhail Zubairy
Edition: 1
Publisher: Oxford University Press
Year: 2020
Language: English
Pages: 304
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
