Quantum Theory of Atomic Structure Volume I2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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Chapter 1．The Historical Development of Modern Physics,from 1900 to Bohr＇s Theory1

1-1．Introduction1

1-2．The Electron and the Nuclear Atom3

1-3．The Development of the Quantum Theory from 1901 to 191312

1-4．The State of Atomic Spectroscopy in 191317

1-5．The Postulates of Bohr＇s Theory of Atomic Structure19

1-6．The Quantum Conditions,and Bohr＇s Theory of Hydrogen22

1-7．Elliptic Orbits,Space Quantization,and Zeeman Effect in Hydrogen26

1-8．Sommerfeld＇s Quantum Condition for the Linear Oscillator27

Chapter 2．Modern Physics from Bohr＇s Theory to Wave Mechanics31

2-1．Introduction31

2-2．Waves and Photons in Optics32

2-3．The Wave Hypothesis of de Broglie35

2-4．Newtonian Mechanics as a Limit of de Broglie＇s Wave Hypothesis37

2-5．Wave Packets and the Uncertainty Principle40

2-6．Schr？dinger＇s Equation44

2-7．Suggested References on Atomic Physics and Quantum Mechanics47

Chapter 3．Schr？dinger＇s Equation and Its Solutions in One-dimensional Problems51

3-1．Hamiltonian Mechanics and Wave Mechanics51

3-2．Schr？dinger＇s Equation,and the Existence of Stationary States54

3-3．Motion of a Particle in a Region of Constant Potential58

3-4．Joining Conditions at a Discontinuity of Potential61

3-5．Wave Functions in a Potential Well,and Other Related Problems65

3-6．The WKB Solution and the Quantum Condition74

3-7．The Linear Oscillator79

3-8．The Numerical Solution of Schr？dinger＇s Equation83

Chapter 4．Average Values and Matrices86

4-1．Introduction86

4-2．The Orthogonality of Eigenfunctions,and the General Solution of Schr？dinger＇s Equation86

4-3．The Average Values of Various Quantities92

4-4．Matrix Components95

4-5．Some Theorems Regarding Matrices98

4-6．Matrix Components for the Linear Oscillator102

4-7．Average Values and the Motion of Wave Packets104

4-8．The Equation of Continuity for the Probability Density105

Chapter 5．The Variation and Perturbation Methods110

5-1．The Variation Principle110

5-2．The Expansion of the Wave Function in Orthogonal Functions113

5-3．The Secular Problem with Two Eigenfunctions119

5-4．The Perturbation Method in the General Case123

5-5．Properties of Unitary Transformations126

Chapter 6．The Interaction of Radiation and Matter131

6-1．The Quantization of the Electromagnetic Field131

6-2．Quantum Statistics and the Average Energy of an Oscillator133

6-3．The Distribution of Modes in the Cavity135

6-4．Einstein＇s Probabilities and the Equilibrium of Radiation and Matter137

6-5．Quantum Theory of the Interaction of Radiation and Matter140

6-6．The Classical Limit for Electromagnetic Problems142

6-7．Hamiltonian and Wave-mechanical Treatment of an Atomic System in a Classical Radiation Field144

6-8．The Method of Variation of Constants for Transition Probabilities148

6-9．The Kramers-Heisenberg Dispersion Formula154

6-10．Dirac＇s Theory of the Interaction of Radiation and Matter158

6-11．The Breadth of Spectrum Lines159

Chapter 7．The Hydrogen Atom166

7-1．Schr？dinger＇s Equation for Hydrogen166

7-2．The Radial Wave Function for Hydrogen170

7-3．The Angular Momentum;Dependence of the Wave Function on Angles177

7-4．Series and Selection Rules182

Chapter 8．The Central-field Model for Atomic Structure188

8-1．Introduction188

8-2．The Postulates of the Central-field Method189

8-3．The Periodic Table of the Elements192

8-4．Spectroscopic Evidence for the Central-field Model196

8-5．An Example of Atomic Spectra:the Sodium Atom199

8-6．Optical and X-ray Energy Levels of the Atoms205

8-7．Dimensions of Electronic Wave Functions in Atoms209

Chapter 9．The Self-consistent-field Method213

9-1．Hartree＇s Assumption for the Atomic Wave Function213

9-2．The Average Hamiltonian for an Atom215

9-3．Energy Integrals for the Hartree Calculation216

9-4．The Hartree Equations as Determined by the Variation Method219

9-5．Examples of Calculation by the Self-consistent-field Method222

9-6．The One-electron and Many-electron Energies of an Atom226

9-7．Inner and Outer Shielding227

9-8．Interpretation of the Rydberg Formula229

Chapter 10．The Vector Model of the Atom234

10-1．Multiplets in Complex Spectra234

10-2．The Russell-Saunders Coupling Scheme239

10-3．The Classical Mechanics of Vector Coupling245

10-4．Landé＇s Theory of Multiplet Separation and the Zeeman Effect249

10-5．General Survey of Wave-mechanical Theory of Multiplet Structure252

Chapter 11．The Behavior of Angular-momentum Vectors in Wave Mechanics255

11-1．The Angular Momentum of an Electron in a Central Field255

11-2．The Precession of the Angular-momentum Vector258

11-3．General Derivation of Matrix Components of Angular Momentum259

11-4．Application of Angular-momentum Properties to Complex Atoms264

11-5．The Nature of Spin-orbitals271

11-6．Use of Angular-momentum Operators in Cases Including Spins274

Chapter 12．Antisymmetry of Wave Functions and the Determinantal Method279

12-1．Wave Functions and Matrix Components of the Hamiltonian for the Two-electron System279

12-2．Symmetric and Antisymmetric Wave Functions,and Pauli＇s Exclusion Principle282

12-3．Spin Coupling in the Two-electron System286

12-4．The Antisymmetric Wave．Function in the N-electron Case288

12-5．Matrix Components of Operators with Respect to Determinantal Wave Functions291

Chapter 13．The Elementary Theory of Multiplets296

13-1．The Secular Problem in Russell-Saunders Coupling296

13-2．Further Examples of the Secular Problem301

13-3．Matrix Components of the Hamiltonian for the Central-field Problem306

13-4．Energy Values for Simple Multiplets312

Chapter 14．Further Results of Multiplet Theory:Closed Shells and Average Energies316

14-1．Closed and Almost Closed Shells316

14-2．The Average Energy of a Configuration322

14-3．Formulation of Multiplet Calculations in Terms of Average Energy326

Chapter 15．Multiplet Calculations for Light Atoms332

15-1．Introduction332

15-2．Experimental Energy Levels of Light Elements337

15-3．Determination of Eav,F2(2p,2p),and G1(2s,2p) from Experiment,Using Least Squares343

15-4．Simple Analytic Models for Wave Functions and Energies of Light Atoms348

15-5．The Self-consistent-field Method for Light Atoms356

15-6．Ionization Potentials and X-ray Energy Levels364

15-7．Simplified Treatment of Light Atoms368

Chapter 16．Multiplet Calculations for Iron-group Elements374

16-1．Introduction374

16-2．Experimental Results on Iron-group Multiplets376

16-3．Self-consistent-field Calculations for the Iron Group:Multiplet Separations383

16-4．Comparison of Theory and Experiment for Total Energy and Ionization Potentials389

Appendix 1．Bohr＇s Theory for Motion in a Central Field395

2． The Principle of Least Action402

3． Wave Packets and Their Motion405

4． Lagrangian and Hamiltonian Methods in Classical Mechanics412

5． The WKB Method420

6． Properties of the Solution of the Linear-oscillator Problem422

7． The Hermitian Character of Matrices426

8． Solution of a Cubic Secular Equation429

9． Orthogonality of Solutions of a Secular Problem430

10． The Correspondence Principle432

11． The Sum Rule for Oscillator Strengths441

12． The Quantum Theory of the Electromagnetic Field443

13． Schr？dinger＇s Equation for the Central-field Problem455

14． Properties of the Associated Legendre Functions457

15． Solutions of the Hydrogen Radial Equation461

16． Bibliography of the Hartree and Hartree-Fock Methods468

17． The Thomas-Fermi Method for Atoms480

18． Commutation Properties of Angular Momenta for Atoms484

19． Positive Nature of Exchange Integrals486

20a．Tabulation of c＇s and a＇s for Multiplet Theory for s,p,and d Electrons488

21a．Tabulation of Energies of Multiplets491

Index495