Quantum Mechanics In A Nutshell

by Mahan, Gerald D.

• ISBN13: 9780691137131
• ISBN10: 0691137137
• Format: Hardcover
• Copyright: 2008-12-29
• Publisher: Princeton Univ Pr

Summary

Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics,Quantum Mechanics in a Nutshellis the distillation of many years' teaching experience.Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original.Quantum Mechanics in a Nutshellexpertly addresses traditional and modern topics, including perturbation theory, WKBJ, variational methods, angular momentum, the Dirac equation, many-particle wave functions, Casimir Force, and Bell's Theorem. And it treats many topics--such as the interactions between photons and electrons, scattering theory, and density functional theory--in exceptional depth.A valuable addition to the teaching literature,Quantum Mechanics in a Nutshellis ideally suited for a two-semester course. The most concise, up-to-date, and accessible graduate textbook on the subject Contains the ideal amount of material for a two-semester course Focuses on the description of actual quantum systems, including a range of applications Covers traditional topics, as well as those at the frontiers of research Treats in unprecedented detail topics such as photon-electron interaction, scattering theory, and density functional theory Includes numerous homework problems at the end of each chapter A solutions manual is available for professors

Table of Contents

Preface xi
Introduction	p. 1
Introduction	p. 1
Schrouml;dinger's Equation	p. 2
Eigenfunctions	p. 4
Measurement	p. 8
Representations	p. 8
Schrouml;dinger Representation	p. 9
Heisenberg Representation	p. 10
Noncommuting Operators	p. 11
One Dimension	p. 14
Square Well	p. 14
Linear Potentials	p. 26
Harmonic Oscillator	p. 29
Raising and Lowering Operators	p. 34
Exponential Potential	p. 39
Bound State	p. 40
Continuum State	p. 42
Delta-Function Potential	p. 45
Number of Solutions	p. 48
Normalization	p. 49
Bound States	p. 49
Box Normalization	p. 50
Delta-Function Normalization	p. 51
The Limit of Infinite Volume	p. 54
Wave Packets	p. 56
Approximate Methods	p. 62
WKBJ	p. 62
Bound States by WKBJ	p. 68
Harmonic Oscillator	p. 71
Morse Potential	p. 71
Symmetric Ramp	p. 73
Discontinuous Potentials	p. 74
Electron Tunneling	p. 76
Variational Theory	p. 77
Half-Space Potential	p. 80
Harmonic Oscillator in One Dimension	p. 82
Spin and Angular Momentum	p. 87
Operators, Eigenvalues, and Eigenfunctions	p. 87
Commutation Relations	p. 88
Raising and Lowering Operators	p. 89
Eigenfunctions and Eigenvalues	p. 90
Representations	p. 95
Rigid Rotations	p. 100
The Addition of Angular Momentum	p. 102
Two and Three Dimensions	p. 108
Plane Waves in Three Dimensions	p. 108
Plane Waves in Two Dimensions	p. 112
Central Potentials	p. 114
Central Potentials in 3D	p. 114
Central Potential in 2D	p. 118
Coulomb Potentials	p. 119
Bound States	p. 119
Confluent Hypergeometric Functions	p. 121
Hydrogen Eigenfunctions	p. 121
Continuum States	p. 125
WKBJ	p. 126
Three Dimensions	p. 126
3D Hydrogen Atom	p. 127
Two Dimensions	p. 128
Hydrogen-like Atoms	p. 130
Quantum Defect	p. 131
WKBJ Derivation	p. 132
Expectation Values	p. 134
Variational Theory	p. 134
Hydrogen Atom:n1	p. 135
Hydrogen Atom:l1	p. 136
Helium Atom	p. 137
Free Particles in a Magnetic Field	p. 143
Gauges	p. 143
Eigenfunctions and Eigenvalues	p. 144
Density of States	p. 146
Quantum Hall Effect	p. 147
Flux Quantization	p. 150
Matrix Methods and Perturbation Theory	p. 157
H and H0	p. 157
Matrix Methods	p. 158
2 x 2	p. 160
Coupled Spins	p. 160
Tight-Binding Model	p. 163
The Stark Effect	p. 166
Perturbation Theory	p. 170
General Formulas	p. 170
Harmonic Oscillator in Electric Field	p. 174
Continuum States	p. 176
Green's Function	p. 180
The Polarizability	p. 181
Quantum Definition	p. 182
Polarizability of Hydrogen	p. 183
Van der Waals Potential	p. 188
Spin-Orbit Interaction	p. 194
Spin-Orbit in Atoms	p. 195
Alkali Valence Electron in Electric Field	p. 199
Bound Particles in Magnetic Fields	p. 202
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