Quantum Mechanics in a Nutshell

by Mahan, Gerald D.

• ISBN13: 9781400833382
• ISBN10: 1400833388
• Copyright: 2010-02-10
• 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	p. xi
Introduction	p. 1
Introduction	p. 1
Schrödinger's Equation	p. 2
Eigenfunctions	p. 4
Measurement	p. 8
Representations	p. 8
Schrödinger 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: n 1	p. 135
Hydrogen Atom: l 1	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
Magnetic Susceptibility	p. 204
Alkali Atom in Magnetic Field	p. 205
Zeeman Effect	p. 207
Paschen-Back Effect	p. 209
Time-Dependent Perturbations	p. 213
Time-Dependent Hamiltonians	p. 213
Sudden Approximation	p. 215
Shake-up and Shake-off	p. 216
Spin Precession	p. 218
Adiabatic Approximation	p. 220
Transition Rates: The Golden Rule	p. 222
Atomic Excitation by a Charged Particle	p. 226
Born Approximation to Scattering	p. 231
Cross Section	p. 232
Rutherford Scattering	p. 235
Electron Scattering from Hydrogen	p. 236
Particle Decay	p. 237
Electromagnetic Radiation	p. 244
Quantization of the Field	p. 245
Gauges	p. 246
Lagrangian	p. 250
Hamiltonian	p. 253
Casimir Force	p. 256
Optical Absorption by a Gas	p. 258
Entangled Photons	p. 268
Oscillator Strength	p. 269
Polarizability	p. 273
Rayleigh and Raman Scattering	p. 278
Compton Scattering	p. 283
Many-Particle Systems	p. 288
Introduction	p. 288
Fermions and Bosons	p. 289
Two Identical Particles	p. 290
Exchange Energy	p. 291
Two-Electron Systems	p. 291
Parahelium and Orthohelium	p. 293
Hund's Rules	p. 293
Many-Electron Systems	p. 295
Evaluating Determinants	p. 295
Ground-State Energy	p. 297
Hartree-Fock Equations	p. 299
Free Electrons	p. 301
Pair Distribution Function	p. 303
Correlation Energy	p. 304
Thomas-Fermi Theory	p. 304
Density Functional Theory	p. 307
Second Quantization	p. 309
Bosons	p. 309
Fermions	p. 312
Bose-Einstein Condensation	p. 313
Noninteracting Particles	p. 313
Off-Diagonal Long-Range Order	p. 314
Scattering Theory	p. 320
Elastic Scattering	p. 320
Partial Wave Analysis	p. 323
Scattering in Two Dimensions	p. 326
Hard-Sphere Scattering	p. 328
Ramsauer-Townsend Effect	p. 330
Born Approximation	p. 332
Scattering of Identical Particles	p. 333
Two Free Particles	p. 333
Electron Scattering from Hydrogen	p. 335
T-Matrices	p. 337
Distorted Wave Scattering	p. 340
Scattering from Many Particles	p. 343
Bragg Scattering	p. 343
Scattering by Fluids	p. 344
Strong Scattering	p. 346
Wave Packets	p. 347
Three Dimensions	p. 347
Scattering by Wave Packets	p. 348
Relativistic Quantum Mechanics	p. 352
Four-Vectors	p. 352
Klein-Gordon Equation	p. 354
Derivation	p. 354
Free Particle	p. 354
Currents and Densities	p. 355
Step Potential	p. 356
Nonrelativistic Limit	p. 356
?-Mesonic Atoms	p. 357
Dirac Equation	p. 360
Derivation	p. 361
Current and Charge Density	p. 364
Gamma-Matrices	p. 364
Free-Particle Solutions	p. 366
Spin-Projection Operators	p. 369
Scattering of Dirac Particles	p. 371
Antiparticles and Negative Energy States	p. 374
Spin Averages	p. 377
Nonrelativistic Limit	p. 379
First Approximation	p. 379
Second Approximation	p. 380
Relativistic Corrections for Hydrogenic States	p. 382
Relativistic Interactions	p. 384
Photon Green's Function	p. 384
Electron Green's Function	p. 387
Boson Exchange	p. 387
Scattering of Electron and Muon	p. 388
Index	p. 397
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