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1 A Review 1

1-1 Newton’s Laws 2

Gravity 3

Hooke’s Law 3

1-2 Work, Energy, and the Conservation of Energy 5

1-3 Rotations and the Center of Mass 8

1-4 Elastic Media and Waves 10

Power and Energy in Waves 13

Reflection and Refraction 14

Coherence, Interference, and Diffraction 14

The Doppler Shift 15

1-5 Thermal Phenomena 16

Kinetic Theory 19

1-6 The Atomic Structure of Matter 21

1-7 Electricity and Magnefism 24

1-8 Electromagnetic Waves and Light 29

Energy and Momentum Transport 32

Polarization 33

Conclusion 33

PART 1 Quantum Mechanics 35

Historical Introduction 35

2 Waves As Particles and Particles As Waves 42

2-1 The Nature of Photons 42

2-2 The Photoelectric Effect 45

2-3 The Compton Effect 49

2-4 Blackbody Radiation 51

2-5 Conceptual Consequences of Light As Particles 55

2-6 Matter Waves and Their Detection 56

Conditions for Interference in Crystals 57

Testing the Wave Character of Electrons 59

2-7 Conceptual Consequences of Particles As Waves 60

Summary 62

Questions 62

Problems 63

3 Atoms and the Bohr Model 67

3-1 The Behavior and Structureof Atoms 67

3-2 The Bohr Atom 69

The Atomic Radius 71

The Atomic Energy 72

Atomic Transitions in the Bohr Model 74

The Franck-Hertz Experiment 78

3-3 Application of Bohr’s Ideas to Other Systems 79

Rotations of Diatomic Molecules 79

The Harmonic Oscillator 82

3-4 The Correspondence Principle 83

Experiments on Nearly Classical Atoms 85

Summary 86

Questions 86

Problems 87

4 The Schrodinger Equation 91

4-1 Wave Functions and Probabilities 91

The Probabilistic Interpretation 94

Towards an Equation for the Wave Function 96

4-2 The Form of the Schrodinger Equation 97

4-3 Expectation Values 99

Normalization 100

Expectation Values 100

4-4 The Time-Independent Schrodinger Equation 103

4-5 An Example: The Infinite Well 104

The Physical Meaning of Eigenfunctions and Eigenvalues 108

4-6 The Schrodinger Equation in Three Dimensions 110

Summary 111

Questions 111

Problems 112

Appendix 115

5 Wave Packets and the Uncertainty Principle 117

5-1 A Free Electron in One Dimension 117

5-2 Wave Packets 121

Making a Pulse 122

The Free Particle Moves 126

5-3 Uncertainty Relations 127

Evaluation of Widths in Position and Momentum 127

The Heisenberg Uncertainty Relation 129

5-4 The Meaning of the UncertaintyRelations 133

The Two-Slit Experiment 136

5-5 The Time-Energy UncertaintyRelation 138

5-6 Estimating Energies 140

Summary 142

Questions 143

Problems 144

6 Barriers and Wells 148

6-1 Particle Motion in the Presence of a Potential Barrier 149

6-2 Wave Functions in the Presence of a Potential Barrier 151

Continuity Conditions 153

Properties of the Solution for E ＞ V0 154

6-3 Tunneling through the Potential Barrier 156

6-4 Applications and Examples of Tunneling 159

Nuclear Physics 159

Molecular Physics 161

Electronics 164

6-5 Bound States 167

Even and Odd Solutions 169

Nodes and Energies 171

Summary 172

Questions 173

Problems 174

Appendix 178

7 Angular Momentum and the Hydrogen Atom 180

7-1 The Schrodinger Equation for Central Potentials 181

Reduction and Partial Solution of the Schrodinger Equation 182

Probabilistic Interpretation of the Wave Function 184

Solving for the Spherical Harmonics 185

7-2 Angular Momentum 189

Eigenvalue Equations for L2 and Lz 190

7-3 Allowed Energies and Electron Spatial Distribution in the Hydrogen Atom 193

Energy Eigenvalues for Hydrogen 194

Radial Eigenfunctions for Hydrogen 196

7-4 The Zeeman Effect 200

The Connection between Magnetic Moments and Angular Momentum 200

Hydrogen in Magnetic Fields and the Zeeman Effect 202

Experimental Observation of the Zeeman Effect 204

The Stern-Gerlach Experiment 204

7-5 Spin 205

The Magnetic Moment of the Electron andthe Anomalous Zeeman Effect 207

Modern Measurement of the Electron g-Factor 209

Addition of Spin and Orbital Angular Momentum 210

Spin-Orbit Coupling 211

7-6 Hyperfine Structure and Magnetic Resonance Imaging 212

Nuclear Magnetic Resonance 214

Summary 216

Questions 217

Problems 218

8 Many Particles 223

8-1 The Multiparticle Schrodinger Equation 223

8-2 Independent Particles 224

8-3 Identical Particles 226

8-4 Exchange Symmetries and the Pauli Principle 229

The Total Spin of Two Electrons 232

Electrons in a Well 233

Exchange Forces 236

8-5 The Fermi Energy 237

Three Dimensions 240

Examples of Degenerate Matter 244

8-6 Degeneracy Pressure 244

A Back-of-the-Envelope Estimate of Degeneracy Pressure 244

A More Accurate Calculation of the Degeneracy Pressure 245

Astrophysical Applications 246

Summary 249

Questions 249

Problems 250

PART 2 Applications 255

9 Complex Atoms and Molecules 256

9-1 Energy in the Helium Atom 256

9-2 Building Up the Periodic Table 258

How to Build Up the Periodic Table 260

9-3 Beyond Z = 10 and General Comments 264

Moseley’s Law and the Auger Effect 267

9-4 Molecules 270

The H2+ Molecule 270

The H2 Molecule and Valence Bonds 272

Ionic Bonding 273

9-5 Nuclear Motion and Its Consequences 274

Vibrations in Molecules 274

Rotations of Molecules 277

Summary 280

Questions 281

Problems 282

10 Statistical Physics 284

10-1 The Description of a Classical Gas 285

10-2 The Maxwell Distribution 289

Experimental Verification of the MaxwellDistribution 292

10-3 The Boltzmann Distribution 293

An Elementary Derivation of the Boltzmann Distribution 294

A System of Molecules with Discrete Energies 296

10-4 Equipartition and Heat Capacity 299

Experiments on Equipartition 304

10-5 The Fermi-Dirac Distribution 305

Identification of the Constants 307

10-6 The Bose-Einstein Distribution 308

10-7 Transition to a Continuum Distribution and the Calculation of Averages 311

The Transition to the Continuum 312

Finding Averages 312

10-8 Systems of Relativistic Particles and the Blackbody Distribution 314

10-9 Some Applications 315

The Specific Heat of Electrons in Metals 315

The Specific Heat of Molecules 316

Bose-Einstein Condensation 317

Liquid Helium and Superfluidity 320

Summary 322

Questions 323

Problems 324

11Decays, Radiation fromAtoms, and Lasers 331

11-1 Decay Rates and Exponential Decay 331

Exponential Decay 332

11-2 The Ingredients of a Quantum Calculation 334

Quantum Mechanical Expression for the Transition Rate 335

Selection Rules 336

11-3 Induced Transitions 337

11-4 Lasers 340

Creating a Population Inversion 342

Pumping Schemes 343

The Cavity 344

Pulses 346

Varieties of Lasers 347

The Gyro Laser 348

Cooling and Trapping of Atoms 350

Optical Tweezers and Scissors 351

Summary 352

Questions 352

Problems 353

12 Conductors,Semiconductors, and Superconductors 356

12-1 The Classical Theory of Conductivity 356

Mean Free Path and Collision Cross Sections 357

The Classical Drude Formula 359

12-2 The Quantum Mechanical Free-elec-tron Model 360

The Quantum Mechanical Speed for the Drude Formula 361

Scattering from a Regular Lattice 362

12-3 Band Structure 366

The Connection between Bands and Propagation in a Lattice 370

The Differences between Conductors and Insulators 374

12-4 Semiconductors 375

Electrons and Holes 377

12-5 Intrinsic and Extrinsic Semiconductors 382

Fermi Energies in Doped Semiconductors 383

12-6 Engineering Applications of Semiconductors: Present and Future 384

Optical Effects in Semiconductors 384

The p-n Junction 386

Transistors 390

Semiconductor Lasers 392

Nanostructures and Integrated Circuits 392

Artificial Atoms 393

12-7 Superconductivity 395

Magnetic Properties of Superconductors 395

Specific Heat and the Superconducting Energy Gap 396

The Bardeen-Cooper-Schrieffer （BCS） Theory 398

Magnetic Flux Quantization 399

High Temperature Superconductors 402

Summary 402

Questions 403

Problems 404

13 The Atomic Nucleus 407

13-1 Neutrons and Protons 407

13-2 Nuclear Size and Mass 410

13-3 The Semiempirical Mass Formula 412

Nuclear Decays 417

13-4 Aspects of Nuclear Structure 419

The Liquid-drop Model 420

The Shell Model 422

13-5 Nuclear Reactions 425

Time Dependence in Quantum Mechanical Decays 425

Nuclear Decay Modes 427

Collision Reactions 431

13-6 Applications 432

Geological and Archeological Dating 432

Nuclear Chain Reactions （Fission） 434

Fusion Reactions 435

Effects of Radiation 436

Summary 437

Questions 438

Problems 439

14 Elementary Particle Physics 444

14-1 Relativistic Quantum Mechanics and Antiparticles 445

14-2 Conservation Laws 448

Does the Proton Decay? 449

14-3 Virtual Particles and a Pictorial Representation 451

Feynman Diagrams 451

Quantum Electrodynamics 453

14-4 The Yukawa Hypothesis and Pions 454

14-5 The Particle “Zoo” and the Discovery of Quarks 458

The Quark Model 461

Quark Confinement and the Experimental Discovery of Quarks 464

14-6 Interactions among the Quarks: Quantum Chromodynamics 465

Heavy Quarks and Quarkonium 467

14-7 Weak Interactions and Leptons 470

Yukawa Hypothesis for the Weak Interactions 473

More Leptons 474

14-8 Pulling Things Together 475

Internal Conservation Laws Revisited 475

The Standard Model 477

Summary 478

Questions 479

Problems 479

Appendix A Tables 485

Appendix B A Mathematical Tool Chest 489

Answers to Odd-Numbered Problems 498

Bibliography 503

Photo Credits 506