Introductory Quantum Physics and Relativity

by Dunningham, Jacob; Vedral, Vlatko

• ISBN13: 9781848165144
• ISBN10: 1848165145
• Format: Hardcover
• Copyright: 2010-10-29
• Publisher: Textstream

Summary

This book is based on the lecture courses taught by Dunningham and Vedral at the University of Leeds. the book contains all the necessary material for quantum physics and relativity in the first two years of a typical physics degree course. the choice of topics complies fully with the Institute of Physics guidelines, but the coverage also includes more interesting and up-to-date applications, such as Bose condensation and quantum teleportation.

Table of Contents

Preface	p. v
Introduction	p. 1
Old Quantum Theory	p. 7
Black Body Radiation	p. 7
The Photoelectric Effect	p. 14
Compton Scattering	p. 16
De Broglie's Hypothesis	p. 18
Bohr's Model of the Atom	p. 20
Problems with Old Quantum Theory	p. 23
Exercises	p. 25
Quantum Mechanics	p. 27
Schrödinger's Equation	p. 28
Born's Postulate	p. 30
Time-Independent Schrödinger Equation	p. 31
Free Particle	p. 33
Observables and Operators	p. 33
The Superposition Principle	p. 35
Expectation Values	p. 36
The Uncertainty Principle	p. 37
Conceptual Foundations of Quantum Mechanics	p. 37
Exercises	p. 41
Applications of Quantum Mechanics	p. 43
Infinite Square Well	p. 43
The Quantum Harmonic Oscillator	p. 46
Tunnelling	p. 48
Reflection and Transmission Coefficients	p. 51
Tunnelling in Action	p. 52
Two Level Systems	p. 54
Cold Matter	p. 55
Exercises	p. 59
Schrödinger Equation in Three-Dimensions	p. 63
Three-Dimensional Box	p. 63
Schrödinger Equation in Spherical Coordinates	p. 64
Separation of Variables	p. 68
The Hydrogen Atom	p. 69
Radial Probability Densities	p. 72
Exercises	p. 74
Spin and Statistics	p. 77
Stern-Gerlach Experiment	p. 77
What is Spin?	p. 79
Symmetry of the Wave Function	p. 80
Wave Function for Two Identical Particles	p. 81
The Pauli Exclusion Principle	p. 83
Spin States and Spin Functions	p. 84
Bose-Einstein and Fermi-Dirac Distributions	p. 85
Exercises	p. 90
Atoms, Molecules and Lasers	p. 91
Periodic Table	p. 91
Ionisation Energies	p. 93
Energy Spectrum	p. 95
Ionic Bonding	p. 95
Covalent Bonding	p. 97
Van der Waals Force	p. 99
Lasers	p. 100
The Lasing Condition	p. 102
Exercises	p. 105
Formal Structure of Quantum Mechanics	p. 107
States and Ensembles	p. 107
Introduction to Dirac Notation	p. 108
Operators	p. 110
Measurements	p. 112
Postulates of Quantum Mechanics	p. 114
Position and Momentum Operators	p. 115
Position and Momentum Wave Functions	p. 116
Fourier Transforms and the Delta Function	p. 117
Position and Momentum Operators Revisited	p. 120
The Schrödinger Equation Revisited	p. 122
The Uncertainty Principle Revisited	p. 123
Pure and Mixed States	p. 124
Annihilation and Creation Operators	p. 126
The Mach-Zehnder Interferometer	p. 128
Perturbation Theory	p. 132
Exercises	p. 136
Second Revolution: Relativity	p. 139
Simultaneity	p. 140
Lorentz Transformations	p. 140
Length Contraction	p. 144
Time Dilation	p. 145
The Twin Paradox	p. 147
Causality	p. 149
E = Mc2	p. 150
Relativistic Newton's Laws of Motion	p. 153
General Relativity	p. 154
Exercises	p. 156
Relativistic Quantum Mechanics	p. 159
Why the Need for Relativistic Quantum Mechanics?	p. 159
The Klein-Gordon Equation	p. 160
Negative Probabilities	p. 161
The Dirac Equation	p. 161
Quantum Field Theory	p. 163
Outlook	p. 166
Exercises	p. 167
Quantum Entanglement	p. 169
What is Entanglement?	p. 170
Bell's Inequalities	p. 171
Quantum Teleportation	p. 174
Why is Entanglement Necessary?	p. 177
The Non-Increase of Entanglement under Local Operations	p. 178
Entanglement Purification	p. 179
Purification of Pure States	p. 182
Entanglement Measures	p. 183
Thermodynamics of Entanglement	p. 186
Quantum Computing	p. 188
Outlook	p. 190
Exercises	p. 192
Solutions	p. 193
Chapter 2	p. 193
Chapter 3	p. 196
Chapter 4	p. 198
Chapter 5	p. 203
Chapter 6	p. 205
Chapter 7	p. 207
Chapter 8	p. 210
Chapter 9	p. 215
Chapter 10	p. 217
Chapter 11	p. 220
Bibliography	p. 223
Index	p. 225
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