Chapter 1．The Historical Development of Modern Physics,from 1900 to Bohr＇s Theory 1
1-1．Introduction 1
1-2．The Electron and the Nuclear Atom 3
1-3．The Development of the Quantum Theory from 1901 to 1913 12
1-4．The State of Atomic Spectroscopy in 1913 17
1-5．The Postulates of Bohr＇s Theory of Atomic Structure 19
1-6．The Quantum Conditions,and Bohr＇s Theory of Hydrogen 22
1-7．Elliptic Orbits,Space Quantization,and Zeeman Effect in Hydrogen 26
1-8．Sommerfeld＇s Quantum Condition for the Linear Oscillator 27
Chapter 2．Modern Physics from Bohr＇s Theory to Wave Mechanics 31
2-1．Introduction 31
2-2．Waves and Photons in Optics 32
2-3．The Wave Hypothesis of de Broglie 35
2-4．Newtonian Mechanics as a Limit of de Broglie＇s Wave Hypothesis 37
2-5．Wave Packets and the Uncertainty Principle 40
2-6．Schr？dinger＇s Equation 44
2-7．Suggested References on Atomic Physics and Quantum Mechanics 47
Chapter 3．Schr？dinger＇s Equation and Its Solutions in One-dimensional Problems 51
3-1．Hamiltonian Mechanics and Wave Mechanics 51
3-2．Schr？dinger＇s Equation,and the Existence of Stationary States 54
3-3．Motion of a Particle in a Region of Constant Potential 58
3-4．Joining Conditions at a Discontinuity of Potential 61
3-5．Wave Functions in a Potential Well,and Other Related Problems 65
3-6．The WKB Solution and the Quantum Condition 74
3-7．The Linear Oscillator 79
3-8．The Numerical Solution of Schr？dinger＇s Equation 83
Chapter 4．Average Values and Matrices 86
4-1．Introduction 86
4-2．The Orthogonality of Eigenfunctions,and the General Solution of Schr？dinger＇s Equation 86
4-3．The Average Values of Various Quantities 92
4-4．Matrix Components 95
4-5．Some Theorems Regarding Matrices 98
4-6．Matrix Components for the Linear Oscillator 102
4-7．Average Values and the Motion of Wave Packets 104
4-8．The Equation of Continuity for the Probability Density 105
Chapter 5．The Variation and Perturbation Methods 110
5-1．The Variation Principle 110
5-2．The Expansion of the Wave Function in Orthogonal Functions 113
5-3．The Secular Problem with Two Eigenfunctions 119
5-4．The Perturbation Method in the General Case 123
5-5．Properties of Unitary Transformations 126
Chapter 6．The Interaction of Radiation and Matter 131
6-1．The Quantization of the Electromagnetic Field 131
6-2．Quantum Statistics and the Average Energy of an Oscillator 133
6-3．The Distribution of Modes in the Cavity 135
6-4．Einstein＇s Probabilities and the Equilibrium of Radiation and Matter 137
6-5．Quantum Theory of the Interaction of Radiation and Matter 140
6-6．The Classical Limit for Electromagnetic Problems 142
6-7．Hamiltonian and Wave-mechanical Treatment of an Atomic System in a Classical Radiation Field 144
6-8．The Method of Variation of Constants for Transition Probabilities 148
6-9．The Kramers-Heisenberg Dispersion Formula 154
6-10．Dirac＇s Theory of the Interaction of Radiation and Matter 158
6-11．The Breadth of Spectrum Lines 159
Chapter 7．The Hydrogen Atom 166
7-1．Schr？dinger＇s Equation for Hydrogen 166
7-2．The Radial Wave Function for Hydrogen 170
7-3．The Angular Momentum;Dependence of the Wave Function on Angles 177
7-4．Series and Selection Rules 182
Chapter 8．The Central-field Model for Atomic Structure 188
8-1．Introduction 188
8-2．The Postulates of the Central-field Method 189
8-3．The Periodic Table of the Elements 192
8-4．Spectroscopic Evidence for the Central-field Model 196
8-5．An Example of Atomic Spectra:the Sodium Atom 199
8-6．Optical and X-ray Energy Levels of the Atoms 205
8-7．Dimensions of Electronic Wave Functions in Atoms 209
Chapter 9．The Self-consistent-field Method 213
9-1．Hartree＇s Assumption for the Atomic Wave Function 213
9-2．The Average Hamiltonian for an Atom 215
9-3．Energy Integrals for the Hartree Calculation 216
9-4．The Hartree Equations as Determined by the Variation Method 219
9-5．Examples of Calculation by the Self-consistent-field Method 222
9-6．The One-electron and Many-electron Energies of an Atom 226
9-7．Inner and Outer Shielding 227
9-8．Interpretation of the Rydberg Formula 229
Chapter 10．The Vector Model of the Atom 234
10-1．Multiplets in Complex Spectra 234
10-2．The Russell-Saunders Coupling Scheme 239
10-3．The Classical Mechanics of Vector Coupling 245
10-4．Landé＇s Theory of Multiplet Separation and the Zeeman Effect 249
10-5．General Survey of Wave-mechanical Theory of Multiplet Structure 252
Chapter 11．The Behavior of Angular-momentum Vectors in Wave Mechanics 255
11-1．The Angular Momentum of an Electron in a Central Field 255
11-2．The Precession of the Angular-momentum Vector 258
11-3．General Derivation of Matrix Components of Angular Momentum 259
11-4．Application of Angular-momentum Properties to Complex Atoms 264
11-5．The Nature of Spin-orbitals 271
11-6．Use of Angular-momentum Operators in Cases Including Spins 274
Chapter 12．Antisymmetry of Wave Functions and the Determinantal Method 279
12-1．Wave Functions and Matrix Components of the Hamiltonian for the Two-electron System 279
12-2．Symmetric and Antisymmetric Wave Functions,and Pauli＇s Exclusion Principle 282
12-3．Spin Coupling in the Two-electron System 286
12-4．The Antisymmetric Wave．Function in the N-electron Case 288
12-5．Matrix Components of Operators with Respect to Determinantal Wave Functions 291
Chapter 13．The Elementary Theory of Multiplets 296
13-1．The Secular Problem in Russell-Saunders Coupling 296
13-2．Further Examples of the Secular Problem 301
13-3．Matrix Components of the Hamiltonian for the Central-field Problem 306
13-4．Energy Values for Simple Multiplets 312
Chapter 14．Further Results of Multiplet Theory:Closed Shells and Average Energies 316
14-1．Closed and Almost Closed Shells 316
14-2．The Average Energy of a Configuration 322
14-3．Formulation of Multiplet Calculations in Terms of Average Energy 326
Chapter 15．Multiplet Calculations for Light Atoms 332
15-1．Introduction 332
15-2．Experimental Energy Levels of Light Elements 337
15-3．Determination of Eav,F2(2p,2p),and G1(2s,2p) from Experiment,Using Least Squares 343
15-4．Simple Analytic Models for Wave Functions and Energies of Light Atoms 348
15-5．The Self-consistent-field Method for Light Atoms 356
15-6．Ionization Potentials and X-ray Energy Levels 364
15-7．Simplified Treatment of Light Atoms 368
Chapter 16．Multiplet Calculations for Iron-group Elements 374
16-1．Introduction 374
16-2．Experimental Results on Iron-group Multiplets 376
16-3．Self-consistent-field Calculations for the Iron Group:Multiplet Separations 383
16-4．Comparison of Theory and Experiment for Total Energy and Ionization Potentials 389
Appendix 1．Bohr＇s Theory for Motion in a Central Field 395
2． The Principle of Least Action 402
3． Wave Packets and Their Motion 405
4． Lagrangian and Hamiltonian Methods in Classical Mechanics 412
5． The WKB Method 420
6． Properties of the Solution of the Linear-oscillator Problem 422
7． The Hermitian Character of Matrices 426
8． Solution of a Cubic Secular Equation 429
9． Orthogonality of Solutions of a Secular Problem 430
10． The Correspondence Principle 432
11． The Sum Rule for Oscillator Strengths 441
12． The Quantum Theory of the Electromagnetic Field 443
13． Schr？dinger＇s Equation for the Central-field Problem 455
14． Properties of the Associated Legendre Functions 457
15． Solutions of the Hydrogen Radial Equation 461
16． Bibliography of the Hartree and Hartree-Fock Methods 468
17． The Thomas-Fermi Method for Atoms 480
18． Commutation Properties of Angular Momenta for Atoms 484
19． Positive Nature of Exchange Integrals 486
20a．Tabulation of c＇s and a＇s for Multiplet Theory for s,p,and d Electrons 488
21a．Tabulation of Energies of Multiplets 491
Index 495