The physics of atoms and quanta : introduction to experiments and theory

목차 (Table of Contents)

• CONTENTS
• List of the Most Important Symbols Used = xv
• 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 Modem 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
• 5.1 Wave Character of Lignt = 49
• 5.2 Thermal 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
• 5.3 The 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 = 67
• 6.1 Production of Free Electrons = 67
• 6.2 Size of the Electron = 67
• 6.3 The Charge of the Electron = 68
• 6.4 The Specific Charge e／m of the Electron = 69
• 6.5 Wave Character of Electrons and Other Particles = 72
• 6.6 Interferometry with Atoms = 76
• Problems = 77
• 7. Some Basic Properties of Matter Waves = 79
• 7.1 Wave Packets = 79
• 7.2 Probabilistic Interpretation = 83
• 7.3 The Heisenberg Uncertainty Relation = 85
• 7.4 The Energy-Time Uncertainty Relation = 87
• 7.5 Some Consequences of the Uncertainty Relations for Bound States = 88
• Problems = 91
• 8. Bohr's Model of the Hydrogen Atom = 93
• 8.1 Basic Principles of Spectroscopy = 93
• 8.2 The Optical Spectrum of the Hydrogen Atom = 95
• 8.3 Bohr's Postulates = 98
• 8.4 Some Quantitative Conclusions = 102
• 8.5 Motion of the Nucleus = 103
• 8.6 Spectra of Hydrogen-like Atoms = 105
• 8.7 Muonie Atoms = 107
• 8.8 Excitation of Quantum Jumps by Collisions = 109
• 8.9 Sommerfeld's Extension of the Bohr Model and the Experimental Justification of a Second Quantum Number = 112
• 8.10 Lifting of Orbital Degeneracy by the Relativistic Mass Change = 113
• 8.11 Limits of the Bohr-Sommerfeld Theory. The Correspondence Principle = 114
• 8.12 Rydberg Atoms = 115
• Problems = 117
• 9. The Mathematical Framework of Quantum Theory = 119
• 9.1 The Particle in a Box = 119
• 9.2 The Schr$$\ddot o$$dinger Equation = 123
• 9.3 The Conceptual Basis of Quantum Theory = 125
• 9.3.1 Observations, Values of Measurements and Operators = 125
• 9.3.2 Momentum Measurement and Momentum Probability = 126
• 9.3.3 Average Values and Expectation Values = 127
• 9.3.4 Operators and Expectation Values = 130
• 9.3.5 Equations for Determining the Wavefunction = 131
• 9.3.6 Simultaneous Observability and Commutation Relations = 133
• 9.4 The Quantum Mechanical Oscillator = 136
• Problems = 142
• 10. Quantum Mechanics of the Hydrogen Atom = 147
• 10.1 Motion in a Central Field = 147
• 10.2 Angular Momentum Eigenfunctions = 149
• 10.3 The Radial Wavefunctions in a Central Field = 155
• 10.4 The Radial Wavefunctions of Hydrogen = 157
• Problems = 163
• 11. Lifting of the Orbital Degeneracy in the Spectra of Alkali Atoms = 165
• 11.1 Shell Structure = 165
• 11.2 Screening = 167
• 11.3 The Term Diagram = 168
• 11.4 Inner Shells = 173
• Problems = 173
• 12. Orbital and Spin Magnetism. Fine Structure = 175
• 12.1 Introduction and Overview = 175
• 12.2 Magnetic Moment of the Orbital Motion = 176
• 12.3 Precession and Orientation in a Magnetic Field = 178
• 12.4 Spin and Magnetic Moment of the Electron = 180
• 12.5 Determination of the Gyromagnetic Ratio by the Einstein-de Haas Method = 182
• 12.6 Detection of Directional Quantisation by Stern and Gerlach = 183
• 12.7 Fine Structure and Spin-Orbit Coupling: Overview = 185
• 12.8 Calculation of Spin-Orbit Splitting in the Bohr Model = 186
• 12.9 Level Scheme of the Alkali Atoms = 190
• 12.10 Fine Structure in the Hydrogen Atom = 191
• 12.11 The Lamb Shift = 192
• Problems = 196
• 13. Atoms in a Magnetic Field: Experiments and Their Semiclassical Description = 199
• 13.1 Directional Quantisation in a Magnetic Field = 199
• 13.2 Electron Spin Resonance = 199
• 13.3 The Zeeman Effect = 202
• 13.3.1 Experiments = 202
• 13.3.2 Explanation of the Zeeman Effect from the Standpoint of Classical Electron Theory = 204
• 13.3.3 Description of the Ordinary Zeeman Effect by the Vector Model = 206
• 13.3.4 The Anomalous Zeeman Effect = 208
• 13.3.5 Magnetic Moments with Spin-Orbit Coupling = 209
• 13.4 The Paschen-Back Effect = 211
• 13.5 Double Resonance and Optical Pumping = 212
• Problems = 214
• 14. Atoms in a Magnetic Field: Quantum Mechanical Treatment = 215
• 14.1 Quantum Theory of the Ordinary Zeeman Effect = 215
• 14.2 Quantum Theoretical Treatment of the Electron and Proton Spins = 217
• 14.2.1 Spin as Angular Momentum = 217
• 14.2.2 Spin Operators, Spin Matrices and Spin Wavefunctions = 218
• 14.2.3 The Schr$$\ddot o$$dinger Equation of a Spin in a Magnetic Field = 220
• 14.2.4 Description of Spin Precession by Expectation Values = 222
• 14.3 Quantum Mechanical Treatment of the Anomalous Zeeman Effect with Spin-Orbit Coupling = 224
• 14.4 Quantum Theory of a Spin in Mutually Perpendicular Magnetic Fields, One Constant and One Time Dependent = 228
• 14.5 The Bloch Equations = 233
• 14.6 The Relativistic Theory of the Electron. The Dirac Equation = 235
• Problems = 241
• 15. Atoms in an Electric Hield = 243
• 15.1 Observations of the Stark Effect = 243
• 15.2 Quantum Theory of the Linear and Quadratic Stark Effects = 245
• 15.2.1 The Hamiltonian = 245
• 15.2.2 The Quadratic Stark Effect. Perturbation Theory Without Degeneracy = 246
• 15.2.3 The Linear Stark Effect. Perturbation Theory in the Presence of Degeneracy = 249
• 15.3 The Interaction of a Two-Level Atom with a Coherent Radiation Field = 252
• 15.4 Spin- and Photon Echoes = 255
• 15.5 A Glance at Quantum Electrodynamics = 258
• 15.5.1 Field Quantization = 258
• 15.5.2 Mass Renormalization and Lamb Shift = 263
• Problems = 270
• 16. General Laws of Optical Transitions = 273
• 16.1 Symmetries and Selection Rules = 273
• 16.1.1 Optical Matrix Elements = 273
• 16.1.2 Examples of the Symmetry Behaviour of Wavefunctions = 273
• 16.1.3 Selection Rules = 278
• 16.1.4 Selection Rules and Multipole Radiation = 281
• 16.2 Linewidths and Lineshapes = 284
• 17. Many-Electron Atoms = 289
• 17.1 The Spectrum of the Helium Atom = 289
• 17.2 Electron Repulsion and the Pauli Principle = 291
• 17.3 Angular Momentum Coupling = 292
• 17.3.1 Coupling Mechanism = 292
• 17.3.2 LS Coupling (Russell-Saunders Coupling) = 292
• 17.3.3 jj Coupling = 296
• 17.4 Magnetic Moments of Many-Electron Atoms = 298
• 17.5 Multiple Excitations = 298
• Problems = 299
• 18. X-Ray Spectra, Internal Shells = 301
• 18.1 Introductory Remarks = 301
• 18.2 X-Radiation from Outer Shells = 301
• 18.3 X-Ray Bremsstrahlung Spectra = 302
• 18.4 Emission Line Spectra: Characteristic Radiation = 304
• 18.5 Fine Structure of the X-Ray Spectra = 306
• 18.6 Absorption Spectra = 308
• 18.7 The Auger Effect = 310
• 18.8 Photoelectron Spectroscopy (XPS), ESCA = 312
• Problems = 313
• 19. Structure of the Periodic System. Ground States of the Elements = 315
• 19.1 Periodic System and Shell Structure = 315
• 19.2 Ground States of Atoms = 322
• 19.3 Excited States and Complete Term Scheme = 324
• 19.4 The Many-Electron Problem. Hartree-Fock Method = 325
• 19.4.1 The Two-Electron Problem = 325
• 19.4.2 Many Electrons Without Mutual Interactions = 330
• 19.4.3 Coulomb Interaction of Electrons. Hartree and Hartree-Fock Methods = 331
• Problems = 334
• 20. Nuclear Spin, Hyperfine Structure = 337
• 20.1 Influence of the Atomic Nucleus on Atomic Spectra = 337
• 20.2 Spins and Magnetic Moments of Atomic Nuclei = 337
• 20.3 The Hyperfine Interaction = 340
• 20.4 Hyperfine Structure in the Ground States of the Hydrogen and Sodium Atoms = 344
• 20.5 Hyperfine Structure in an External Magnetic Field, Electron Spin Resonance = 346
• 20.6 Direct Measurements of Nuclear Spins and Magnetic Moments, Nuclear Magnetic Resonance = 350
• 20.7 Applications of Nuclear Magnetic Resonance = 354
• 20.8 The Nuclear Electric Quadrupole Moment = 359
• Problems = 361
• 21. The Laser = 363
• 21.1 Some Basic Concepts for the Laser = 363
• 21.2 Rate Equations and Lasing Conditions = 366
• 21.3 Amplitude and Phase of Laser Light = 369
• Problems = 372
• 22. Modern Methods of Optical Spectroscopy = 375
• 22.1 Classical Methods = 375
• 22.2 Quantum Beats = 376
• 22.3 Doppler-free Saturation Spectroscopy = 378
• 22.4 Doppler-free Two-Photon Absorption = 380
• 22.5 Level-Crossing Spectroscopy and the Hanle Effect = 382
• 22.6 Laser Cooling of Atoms = 384
• 23. Fundamentals of the Quantum Theory of Chemical Bonding = 389
• 23.1 Introductory Remarks = 389
• 23.2 The Hydrogen-Molecule Ion $$H^+_2$$ = 389
• 23.3 The Tunnel Effect = 395
• 23.4 The Hydrogen Molecule $$H_2$$ = 397
• 23.5 Covalent-Ionic Resonance = 404
• 23.6 The Hund-Mulliken-Bloch Theory of Bonding in Hydrogen = 405
• 23.7 Hybridisation = 406
• 23.8 The $$\pi$$ Electrons of Benzene, $$C_6H_6$$ = 408
• Problems = 410
• Appendix = 411
• A. The Dirac Delta Function and the Normalisation of the Wavefunction of a Free Particle in Unbounded Space = 411
• B. Some Properties of the Hamiltonian Operator, Its Eigenfunctions and Its Eigenvalues = 415
• C. Derivation of Heisenberg's Uncertainty Relation = 416
• Solutions to the Problems = 419
• Bibliography of Supplementary and Specialised Literature = 449
• Subject Index = 453
• Fundamental Constants of Atomic Physics (Inside Front Cover)
• Energy Conversion Table (Inside Back Cover)