简明量子力学 英文PDF|Epub|txt|kindle电子书版本网盘下载

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1 Introduction1

1.1 Introduction1

1.2 Schr？dinger's Equation2

1.3 Eigenfunctions4

1.4 Measurement8

1.5 Representations8

1.5.1 Schr？dinger Representation9

1.5.2 Heisenberg Representation10

1.6 Noncommuting Operators11

2 One Dimension14

2.1 Square Well14

2.2 Linear Potentials26

2.3 Harmonic Oscillator29

2.4 Raising and Lowering Operators34

2.5 Exponential Potential39

2.5.1 Bound State40

2.5.2 Continuum State42

2.6 Delta-Function Potential45

2.7 Number of Solutions48

2.8 Normalization49

2.8.1 Bound States49

2.8.2 Box Normalization50

2.8.3 Delta-Function Normalization51

2.8.4 The Limit of Infinite Volume54

2.9 Wave Packets56

3 Approximate Methods62

3.1 WKBJ62

3.2 Bound States by WKBJ68

3.2.1 Harmonic Oscillator71

3.2.2 Morse Potential71

3.2.3 Symmetric Ramp73

3.2.4 Discontinuous Potentials74

3.3 Electron Tunneling76

3.4 Variational Theory77

3.4.1 Half-Space Potential80

3.4.2 Harmonic Oscillator in One Dimension82

4 Spin Angular Momentum87

4.1 Operators, Eigenvalues, and Eigenfunctions87

4.1.1 Commutation Relations88

4.1.2 Raising and Lowering Operators89

4.1.3 Eigenfunctions and Eigenvalues90

4.2 Representations95

4.3 Rigid Rotations100

4.4 The Addition of Angular Momentum102

5 Two and Three Dimensions108

5.1 Plane Waves in Three Dimensions108

5.2 Plane Waves in Two Dimensions112

5.3 Central Potentials114

5.3.1 Central Potentials in 3D114

5.3.2 Central Potential in 2D118

5.4 Coulomb Potentials119

5.4.1 Bound States119

5.4.2 Confluent Hypergeometric Functions121

5.4.3 Hydrogen Eigenfunctions121

5.4.4 Continuum States125

5.5 WKBJ126

5.5.1 Three Dimensions126

5.5.2 3D Hydrogen Atom127

5.5.3 Two Dimensions128

5.6 Hydrogen-like Atoms130

5.6.1 Quantum Defect131

5.6.2 WKBJ Derivation132

5.6.3 Expectation Values134

5.7 Variational Theory134

5.7.1 Hydrogen Atom: n=1135

5.7.2 Hydrogen Atom: e=1136

5.7.3 Helium Atom137

5.8 Free Particles in a Magnetic Field143

5.8.1 Gauges143

5.8.2 Eigenfunctions and Eigenvalues144

5.8.3 Density of States146

5.8.4 Quantum Hall Effect147

5.8.5 Flux Quantization150

6 Matrix Methods and Perturbation Theory157

6.1 H and H0157

6.2 Matrix Methods158

6.2.1 2×2160

6.2.2 Coupled Spins160

6.2.3 Tight-Binding Model163

6.3 The Stark Effect166

6.4 Perturbation Theory170

6.4.1 General Formulas170

6.4.2 Harmonic Oscillator in Electric Field174

6.4.3 Continuum States176

6.4.4 Green's Function180

6.5 The Polarizability181

6.5.1 Quantum Definition182

6.5.2 Polarizability of Hydrogen183

6.6 Van der Waals Potential188

6.7 Spin-Orbit Interaction194

6.7.1 Spin-Orbit in Atoms195

6.7.2 Alkali Valence Electron in Electric Field199

6.8 Bound Particles in Magnetic Fields202

6.8.1 Magnetic Susceptibility204

6.8.2 Alkali Atom in Magnetic Field205

6.8.3 Zeeman Effect207

6.8.4 Paschen-Back Effect209

7 Time-Dependent Perturbations213

7.1 Time-Dependent Hamiltonians213

7.2 Sudden Approximation215

7.2.1 Shake-up and Shake-off216

7.2.2 Spin Precession218

7.3 Adiabatic Approximation220

7.4 Transition Rates: The Golden Rule222

7.5 Atomic Excitation by a Charged Particle226

7.6 Born Approximation to Scattering231

7.6.1 Cross Section232

7.6.2 Rutherford Scattering235

7.6.3 Electron Scattering from Hydrogen236

7.7 Particle Decay237

8 Electromagnetic Radiation244

8.1 Quantization of the Field245

8.1.1 Gauges246

8.1.2 Lagrangian250

8.1.3 Hamiltonian253

8.1.4 Casimir Force256

8.2 Optical Absorption by a Gas258

8.2.1 Entangled Photons268

8.3 Oscillator Strength269

8.4 Polarizability273

8.5 Rayleigh and Raman Scattering278

8.6 Compton Scattering283

9 Many-Particle Systems288

9.1 Introduction288

9.2 Fermions and Bosons289

9.2.1 Two Identical Particles290

9.3 Exchange Energy291

9.3.1 Two-Electron Systems291

9.3.2 Parahelium and Orthohelium293

9.3.3 Hund's Rules293

9.4 Many-Electron Systems295

9.4.1 Evaluating Determinants295

9.4.2 Ground-State Energy297

9.4.3 Hartree-Fock Equations299

9.4.4 Free Electrons301

9.4.5 Pair Distribution Function303

9.4.6 Correlation Energy304

9.4.7 Thomas-Fermi Theory304

9.4.8 Density Functional Theory307

9.5 Second Quantization309

9.5.1 Bosons309

9.5.2 Fermions312

9.6 Bose-Einstein Condensation313

9.6.1 Noninteracting Particles313

9.6.2 Off-Diagonal Long-Range Order314

10 Scattering Theory320

10.1 Elastic Scattering320

10.1.1 Partial Wave Analysis323

10.1.2 Scattering in Two Dimensions326

10.1.3 Hard-Sphere Scattering328

10.1.4 Ramsauer-Townsend Effect330

10.1.5 Born Approximation332

10.2 Scattering of Identical Particles333

10.2.1 Two Free Particles333

10.2.2 Electron Scattering from Hydrogen335

10.3 T-Matrices337

10.4 Distorted Wave Scattering340

10.5 Scattering from Many Particles343

10.5.1 Bragg Scattering343

10.5.2 Scattering by Fluids344

10.5.3 Strong Scattering346

10.6 Wave Packets347

10.6.1 Three Dimensions347

10.6.2 Scattering by Wave Packets348

11 Relativistic Quantum Mechanics352

11.1 Four-Vectors352

11.2 Klein-Gordon Equation354

11.2.1 Derivation354

11.2.2 Free Particle354

11.2.3 Currents and Densities355

11.2.4 Step Potential356

11.2.5 Nonrelativistic Limit356

11.2.6 п-Mesonic Atoms357

11.3 Dirac Equation360

11.3.1 Derivation361

11.3.2 Current and Charge Density364

11.3.3 Gamma-Matrices364

11.3.4 Free-Particle Solutions366

11.3.5 Spin-Projection Operators369

11.3.6 Scattering of Dirac Particles371

11.4 Antiparticles and Negative Energy States374

11.5 Spin Averages377

11.6 Nonrelativistic Limit379

11.6.1 First Approximation379

11.6.2 Second Approximation380

11.6.3 Relativistic Corrections for Hydrogenic States382

11.7 Relativistic Interactions384

11.7.1 Photon Green's Function384

11.7.2 Electron Green's Function387

11.7.3 Boson Exchange387

11.8 Scattering of Electron and Muon388