内容

目次

Preface xi Chapter 1: Introduction 1 1.1 Introduction 1 1.2Schrodinger's Equation 2 1.3 Eigenfunctions 4 1.4 Measurement 8 1.5Representations 8 1.5.1 Schrodinger Representation 9 1.5.2 HeisenbergRepresentation 10 1.6 Noncommuting Operators 11 Chapter 2: OneDimension 14 2.1 Square Well 14 2.2 Linear Potentials 26 2.3 HarmonicOscillator 29 2.4 Raising and Lowering Operators 34 2.5 ExponentialPotential 39 2.5.1 Bound State 40 2.5.2 Continuum State 42 2.6Delta-Function Potential 45 2.7 Number of Solutions 48 2.8 Normalization 492.8.1 Bound States 49 2.8.2 Box Normalization 50 2.8.3 Delta-FunctionNormalization 51 2.8.4 The Limit of Infinite Volume 54 2.9 Wave Packets 56Chapter 3: Approximate Methods 62 3.1 WKBJ 62 3.2 Bound States by WKBJ68 3.2.1 Harmonic Oscillator 71 3.2.2 Morse Potential 71 3.2.3Symmetric Ramp 73 3.2.4 Discontinuous Potentials 74 3.3 Electron Tunneling76 3.4 Variational Theory 77 3.4.1 Half-Space Potential 80 3.4.2Harmonic Oscillator in One Dimension 82 Chapter 4: Spin and AngularMomentum 87 4.1 Operators, Eigenvalues, and Eigenfunctions 87 4.1.1Commutation Relations 88 4.1.2 Raising and Lowering Operators 89 4.1.3Eigenfunctions and Eigenvalues 90 4.2 Representations 95 4.3 RigidRotations 100 4.4 The Addition of Angular Momentum 102 Chapter 5: Twoand Three Dimensions 108 5.1 Plane Waves in Three Dimensions 108 5.2 PlaneWaves in Two Dimensions 112 5.3 Central Potentials 114 5.3.1 CentralPotentials in 3D 114 5.3.2 Central Potential in 2D 118 5.4 CoulombPotentials 119 5.4.1 Bound States 119 5.4.2 Confluent HypergeometricFunctions 121 5.4.3 Hydrogen Eigenfunctions 121 5.4.4 Continuum States125 5.5 WKBJ 126 5.5.1 Three Dimensions 126 5.5.2 3D Hydrogen Atom 1275.5.3 Two Dimensions 128 5.6 Hydrogen-like Atoms 130 5.6.1 Quantum Defect131 5.6.2 WKBJ Derivation 132 5.6.3 Expectation Values 134 5.7Variational Theory 134 5.7.1 Hydrogen Atom: n 1 135 5.7.2 Hydrogen Atom:l 1 136 5.7.3 Helium Atom 137 5.8 Free Particles in a Magnetic Field 1435.8.1 Gauges 143 5.8.2 Eigenfunctions and Eigenvalues 144 5.8.3 Densityof States 146 5.8.4 Quantum Hall Effect 147 5.8.5 Flux Quantization 150Chapter 6: Matrix Methods and Perturbation Theory 157 6.1 H and H0 1576.2 Matrix Methods 158 6.2.1 2 x 2 160 6.2.2 Coupled Spins 160 6.2.3Tight-Binding Model 163 6.3 The Stark Effect 166 6.4 Perturbation Theory170 6.4.1 General Formulas 170 6.4.2 Harmonic Oscillator in ElectricField 174 6.4.3 Continuum States 176 6.4.4 Green's Function 180 6.5 ThePolarizability 181 6.5.1 Quantum Definition 182 6.5.2 Polarizability ofHydrogen 183 6.6 Van der Waals Potential 188 6.7 Spin-Orbit Interaction 1946.7.1 Spin-Orbit in Atoms 195 6.7.2 Alkali Valence Electron in ElectricField 199 6.8 Bound Particles in Magnetic Fields 202 6.8.1 MagneticSusceptibility 204 6.8.2 Alkali Atom in Magnetic Field 205 6.8.3 ZeemanEffect 207 6.8.4 Paschen-Back Effect 209 Chapter 7: Time-DependentPerturbations 213 7.1 Time-Dependent Hamiltonians 213 7.2 SuddenApproximation 215 7.2.1 Shake-up and Shake-off 216 7.2.2 Spin Precession218 7.3 Adiabatic Approximation 220 7.4 Transition Rates: The Golden Rule222 7.5 Atomic Excitation by a Charged Particle 226 7.6 Born Approximationto Scattering 231 7.6.1 Cross Section 232 7.6.2 Rutherford Scattering 2357.6.3 Electron Scattering from Hydrogen 236 7.7 Particle Decay 237Chapter 8: Electromagnetic Radiation 244 8.1 Quantization of the Field 2458.1.1 Gauges 246 8.1.2 Lagrangian 250 8.1.3 Hamiltonian 253 8.1.4Casimir Force 256 8.2 Optical Absorption by a Gas 258 8.2.1 EntangledPhotons 268 8.3 Oscillator Strength 269 8.4 Polarizability 273 8.5Rayleigh and Raman Scattering 278 8.6 Compton Scattering 283 Chapter 9:Many-Particle Systems 288 9.1 Introduction 288 9.2 Fermions and Bosons 2899.2.1 Two Identical Particles 290 9.3 Exchange Energy 291 9.3.1Two-Electron Systems 291 9.3.2 Parahelium and Orthohelium 293 9.3.3Hund's Rules 293 9.4 Many-Electron Systems 295 9.4.1 EvaluatingDeterminants 295 9.4.2 Ground-State Energy 297 9.4.3 Hartree-FockEquations 299 9.4.4 Free Electrons 301 9.4.5 Pair Distribution Function303 9.4.6 Correlation Energy 304 9.4.7 Thomas-Fermi Theory 304 9.4.8Density Functional Theory 307 9.5 Second Quantization 309 9.5.1 Bosons 3099.5.2 Fermions 312 9.6 Bose-Einstein Condensation 313 9.6.1Noninteracting Particles 313 9.6.2 Off-Diagonal Long-Range Order 314Chapter 10: Scattering Theory 320 10.1 Elastic Scattering 320 10.1.1Partial Wave Analysis 323 10.1.2 Scattering in Two Dimensions 326 10.1.3Hard-Sphere Scattering 328 10.1.4 Ramsauer-Townsend Effect 330 10.1.5Born Approximation 332 10.2 Scattering of Identical Particles 333 10.2.1Two Free Particles 333 10.2.2 Electron Scattering from Hydrogen 335 10.3T-Matrices 337 10.4 Distorted Wave Scattering 340 10.5 Scattering from ManyParticles 343 10.5.1 Bragg Scattering 343 10.5.2 Scattering by Fluids 34410.5.3 Strong Scattering 346 10.6 Wave Packets 347 10.6.1 ThreeDimensions 347 10.6.2 Scattering by Wave Packets 348 Chapter 11:Relativistic Quantum Mechanics 352 11.1 Four-Vectors 352 11.2 Klein-GordonEquation 354 11.2.1 Derivation 354 11.2.2 Free Particle 354 11.2.3Currents and Densities 355 11.2.4 Step Potential 356 11.2.5Nonrelativistic Limit 356 11.2.6 ?-Mesonic Atoms 357 11.3 Dirac Equation360 11.3.1 Derivation 361 11.3.2 Current and Charge Density 364 11.3.3Gamma-Matrices 364 11.3.4 Free-Particle Solutions 366 11.3.5Spin-Projection Operators 369 11.3.6 Scattering of Dirac Particles 37111.4 Antiparticles and Negative Energy States 374 11.5 Spin Averages 37711.6 Nonrelativistic Limit 379 11.6.1 First Approximation 379 11.6.2Second Approximation 380 11.6.3 Relativistic Corrections for HydrogenicStates 382 11.7 Relativistic Interactions 384 11.7.1 Photon Green'sFunction 384 11.7.2 Electron Green's Function 387 11.7.3 Boson Exchange387 11.8 Scattering of Electron and Muon 388 Index 397