1. Introduction 1
1.1 Classical Physics and Quantum Mechanics 1
1.2 Short Historical Review 1
2. The Mass and Size of the Atom 5
2.1 What is an Atom? 5
2.2 Determination of the Mass 5
2.3 Methods for Determining Avogadro’s Number 7
2.3.1 Electrolysis 7
2.3.2 The Gas Constant and Boltzmann’s Constant 7
2.3.3 X-Ray Diffraction in Crystals 8
2.3.4 Determination Using Radioactive Decay 9
2.4 Determination of the Size of the Atom 10
2.4.1 Application of the Kinetic Theory of Gases 10
2.4.2 The Interaction Cross Section 11
2.4.3 Experimental Determination of Interaction Cross Sections 14
2.4.4 Determining the Atomic Size from the Covolume 15
2.4.5 Atomic Sizes from X-Ray Diffraction Measurements on Crystals 15
2.4.6 Can Individual Atoms Be Seen? 20
Problems 25
3. Isotopes 27
3.1 The Periodic System of the Elements 27
3.2 Mass Spectroscopy 29
3.2.1 Parabola Method 29
3.2.2 Improved Mass Spectrometers 32
3.2.3 Results of Mass Spectrometry 33
3.2.4 Modern Applications of the Mass Spectrometer 34
3.2.5 Isotope Separation 35
Problems 36
4. The Nucleus of the Atom 37
4.1 Passage of Electrons Through Matter 37
4.2 Passage of Alpha Particles Through Matter（Rutherford Scattering） 39
4.2.1 Some Properties of Alpha Particles 39
4.2.2 Scattering of Alpha Particles by a Foil 39
4.2.3 Derivation of the Rutherford Scattering Formula 41
4.2.4 Experimental Results 46
4.2.5 What is Meant by Nuclear Radius? 47
Problems 48
5. The Photon 49
5.1Wave Character of Light 49
5.2Thermal Radiation 51
5.2.1 Spectral Distribution of Black Body Radiation 51
5.2.2 Planck’s Radiation Formula 53
5.2.3 Einstein’s Derivation of Planck’s Formula 54
5.3The Photoelectric Effect 58
5.4 The Compton Effect 60
5.4.1 Experiments 60
5.4.2 Derivation of the Compton Shift 62
Problems 64
6. The Electron 69
6.1 Production of Free Electrons 69
6.2 Size of the Electron 69
6.3 The Charge of the Electron 70
6.4 The Specific Charge e/m of the Electron 71
6.5 Wave Character of Electrons and Other Particles 74
6.6 Interferometry with Atoms 78
Problems 79
7. Some Basic Properties of Matter Waves 81
7.1 Wave Packets 81
7.2 Probabilistic Interpretation 85
7.3 The Heisenberg Uncertainty Relation 87
7.4 The Energy-Time Uncertainty Relation 89
7.5 Some Consequences of the Uncertainty Relations for Bound States 90
Problems 93
8. Bohr’s Model of the Hydrogen Atom 95
8.1 Basic Principles of Spectroscopy 95
8.2 The Optical Spectrum of the Hydrogen Atom 97
8.3 Bohr’s Postulates 100
8.4 Some Quantitative Conclusions 104
8.5 Motion of the Nucleus 105
8.6 Spectra of Hydrogen-like Atoms 107
8.7 Muonic Atoms 109
8.8 Excitation of Quantum Jumps by Collisions 111
8.9 Sommerfeld’s Extension of the Bohr Model and the Experimental Justification of a Second Quantum Number 114
8.10 Lifting of Orbital Degeneracy by the Relativistic Mass Change 115
8.11 Limits of the Bohr-Sommerfeld Theory.The Correspondence Principle 116
8.12 Rydberg Atoms 117
8.13 Positronium，Muonium，and Antihydrogen 119
Problems 121
9. The Mathematical Framework of Quantum Theory 125
9.1The Particle in a Box 125
9.2The Schr?dinger Equation 129
9.3. The Conceptual Basis of Quantum Theory 131
9.3.1 Observations， Values of Measurements and Operators 131
9.3.2 Momentum Measurement and Momentum Probability 132
9.3.3 Average Values and Expectation Values 133
9.3.4 Operators and Expectation Values 136
9.3.5 Equations for Determining the Wavefunction 137
9.3.6 Simultaneous Observability and Commutation Relations 139
9.4.The Quantum Mechanical Oscillator 142
Problems 148
10. Quantum Mechanics of the Hydrogen Atom 153
10.1 Motion in a Central Field 153
10.2 Angular Momentum Eigenfunctions 155
10.3 The Radial Wavefunctions in a Central Field 161
10.4 The Radial Wavefunctions of Hydrogen 163
Problems 169
11. Lifting of the Orbital Degeneracy in the Spectra of Alkali Atoms 171
11.1 Shell Structure 171
11.2 Screening 173
11.3 The Term Diagram 174
11.4 Inner Shells 179
Problems 179
12. Orbital and Spin Magnetism. Fine Structure 181
12.1 Introduction and Overview 181
12.2 Magnetic Moment of the Orbital Motion 182
12.3 Precession and Orientation in a Magnetic Field 184
12.4 Spin and Magnetic Moment of the Electron 186
12.5 Determination of the Gyromagnetic Ratio by the Einstein-de Haas Method 188
12.6 Detection of Directional Quantisation by Stern and Gerlach 189
12.7 Fine Structure and Spin-Orbit Coupling： Overview 191
12.8 Calculation of Spin-Orbit Splitting in the Bohr Model 192
12.9 Level Scheme of the Alkali Atoms 196
12.10 Fine Structure in the Hydrogen Atom 197
12.11 The Lamb Shift 198
Problems 202
13. Atoms in a Magnetic Field：Experiments and Their Semiclassical Description 205
13.1 Directional Quantisation in a Magnetic Field 205
13.2 Electron Spin Resonance 205
13.3 The Zeeman Effect 208
13.3.1 Experiments 208
13.3.2 Explanation of the Zeeman Effect from the Standpoint of Classical Electron Theory 210
13.3.3 Description of the Ordinary Zeeman Effect by the Vector Model 212
13.3.4 The Anomalous Zeeman Effect 214
13.3.5 Magnetic Moments with Spin-Orbit Coupling 215
13.4 The Paschen-Back Effect 217
13.5 Double Resonance and Optical Pumping 218
Problems 220
14. Atoms in a Magnetic Field：Quantum Mechanical Treatment 223
14.1 Quantum Theory of the Ordinary Zeeman Effect 223
14.2 Quantum Theoretical Treatment of the Electron and Proton Spins 225
14.2.1 Spin as Angular Momentum 225
14.2.2 Spin Operators，Spin Matrices and Spin Wavefunctions 226
14.2.3 The Schr?dinger Equation of a Spin in a Magnetic Field 228
14.2.4 Description of Spin Precession by Expectation Values 230
14.3 Quantum Mechanical Treatment of the Anomalous Zeeman Effect with Spin-Orbit Coupling 232
14.4 Quantum Theory of a Spin in Mutually Perpendicular Magnetic Fields，One Constant and One Time Dependent 236
14.5 The Bloch Equations 241
14.6 The Relativistic Theory of the Electron. The Dirac Equation 243
Problems 249
15. Atoms in an Electric Field 251
15.1 Observations of the Stark Effect 251
15.2 Quantum Theory of the Linear and Quadratic Stark Effects 253
15.2.1 The Hamiltonian 253
15.2.2 The Quadratic Stark Effect.Perturbation Theory Without Degeneracy 254
15.2.3 The Linear Stark Effect.Perturbation Theory in the Presence of Degeneracy 257
15.3 The Interaction of a Two-Level Atom with a Coherent Radiation Field 260
15.4 Spin and Photon Echoes 263
15.5 A Glance at Quantum Electrodynamics 266
15.5.1 Field Quantization 266
15.5.2 Mass Renormalization and Lamb Shift 271
Problems 278
16. General Laws of Optical Transitions 281
16.1 Symmetries and Selection Rules 281
16.1.1 Optical Matrix Elements 281
16.1.2 Examples of the Symmetry Behaviour of Wavefunctions 281
16.1.3 Selection Rules 286
16.1.4 Selection Rules and Multipole Radiation 289
16.2 Linewidths and Lineshapes 292
17. Many-Electron Atoms 297
17.1 The Spectrum of the Helium Atom 297
17.2 Electron Repulsion and the Pauli Principle 299
17.3 Angular Momentum Coupling 300
17.3.1 Coupling Mechanism 300
17.3.2 LS Coupling（Russell-Saunders Coupling） 300
17.3.3 jj Coupling 304
17.4 Magnetic Moments of Many-Electron Atoms 306
17.5 Multiple Excitations 307
Problems 307
18. X-Ray Spectra，Internal Shells 309
18.1 Introducto Remarks 309
18.2 X-Radiation from Outer Shells 309
18.3 X-Ray Bremsstrahlung Spectra 310
18.4 Emission Line Spectra： Characteristic Radiation 312
18.5 Fine Structure of the X-Ray Spectra 314
18.6 Absorption Spectra 316
18.7 The Auger Effect 318
18.8 Photoelectron Spectroscopy（XPS），ESCA 320
Problems 322
19. Structure of the Periodic System.Ground States of the Elements 323
19.1 Periodic System and Shell Structure 323
19.2 From the Electron Configuration to the Atomic Term Scheme.Atomic Ground States 330
19.3 Excited States of Atoms and Possible Electronic Configurations.Complete Term Schemes 333
19.4 The Many-Electron Problem. Hartree-Fock Method 335
19.4.1 The Two-Electron Problem 335
19.4.2 Many Electrons Without Mutual Interactions 340
19.4.3 Coulomb Interaction of Electrons.Hartree and Hartree-Fock Methods 341
Problems 344
20. Nuclear Spin，Hyperfine Structure 347
20.1 Influence of the Atomic Nucleus on Atomic Spectra 347
20.2 Spins and Magnetic Moments of Atomic Nuclei 348
20.3 The Hyperfine Interaction 350
20.4 Hyperfine Structure in the Ground State of the Hydrogen Atom，the Sodium Atom，and the Hydrogen-like Ion 83Bi82﹢ 354
20.5 Hyperfine Structure in an External Magnetic Field，Electron Spin Resonance 356
20.6 Direct Measurements of Nuclear Spins and Magnetic Moments，Nuclear Magnetic Resonance 361
20.7 Applications of Nuclear Magnetic Resonance 364
20.8 The Nuclear Electric Quadrupole Moment 369
Problems 371
21. The Laser 373
21.1 Some Basic Concepts for the Laser 373
21.2 Rate Equations and Lasing Conditions 376
21.3 Amplitude and Phase of Laser Light 379
Problems 382
22. Modern Methods of Optical Spectroscopy 385
22.1 Classical Methods 385
22.2 Quantum Beats 386
22.3 Doppler-free Saturation Spectroscopy 388
22.4 Doppler-free Two-Photon Absorption 390
22.5 Level-Crossing Spectroscopy and the Hanle Effect 392
22.6 Laser Cooling of Atoms 394
22.7 Nondestructive Single-Photon Detection An Example of Atomic Physics in a Resonant Cavity 399
Problems 401
23. Progress in Quantum Physics：A Deeper Understanding and New Applications 403
23.1 Introduction 403
23.2 The Superposition Principle，Interference，Probabilily and Probability Amplitudes 403
23.3 Schr?dinger’s Cat 405
23.4 Decoherence 405
23.5 Entanglement 406
23.6 The Einstein-Podolsky-Rosen（EPR）Paradox 407
23.7 Bell’s Inequalities and the Hidden-Variable Hypothesis 408
23.8 Experiments to Test Bell’s Inequalities 411
23.9 Quantum Computers 412
23.9.1 Historical Remarks 412
23.9.2 Review of Digital Computers 413
23.9.3 Basic Concepts of the Quantum Computer 414
23.9.4 Decoherence and Error Correction 416
23.9.5 A Comparison Between the Quantum Computer and the Digital Computer 418
23.10 Quantum Information Theory 418
23.11 The Bose-Einstein Condensation 418
23.11.1 Review of Statistical Mechanics 418
23.11.2 The Experimental Discovery 419
23.11.3 The Quantum Theory of the Bose-Einstein Condensation 421
23.12 The Atom Laser 422
Problems 423
24. Fundamentals of the Quantum Theory of Chemical Bonding 425
24.1Introductory Remarks 425
24.2 The Hydrogen-Molecule Ion H﹢2 425
24.3 The Tunnel Effect 431
24.4 The Hydrogen Molecule H2 433
24.5Covalent-Ionic Resonance 440
24.6 The Hund-Mulliken-Bloch Theory of Bonding in Hydrogen 441
24.7Hybridisation 442
24.8 The π Electrons of Benzene，C6H6 444
Problems 446
Appendix 447
A. The Dirac Delta Function and the Normalisation of the Wavefunction of a Free Particle in Unbounded Space 447
B. Some Properties of the Hamiltonian Operator， Its Eigenfunctions and its Eigenvalues 451
C. Derivation of Heisenberg’s Uncertainty Relation 452
Solutions to the Problems 455
Bibliography of Supplementary and Specialised Literature 485
Subject Index 493