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Description
This modern textbook offers an introduction to Quantum Mechanics as a theory that underlies the world around us, from atoms and molecules to materials, lasers, and other applications.
The main features of the book are:
- Emphasis on the key principles with minimal mathematical formalism
- Demystifying discussions of the basic features of quantum systems, using dimensional analysis and order-of-magnitude estimates to develop intuition
- Comprehensive overview of the key concepts of quantum chemistry and the electronic structure of solids
- Extensive discussion of the basic processes and applications of light-matter interactions
- Online supplement with advanced theory, multiple-choice quizzes, etc.
Table of Contents
Foreword xix
Preface xxiii
Editors' Note xxvii
Part I Fundamental Principles 1
1 The Principle of Wave–Particle Duality: An Overview 3
1.1 Introduction 3
1.2 The Principle of Wave–Particle Duality of Light 4
1.3 The Principle of Wave–Particle Duality of Matter 11
1.4 Dimensional Analysis and Quantum Physics 41
2 The Schrödinger Equation and Its Statistical Interpretation 53
2.1 Introduction 53
2.2 The Schrödinger Equation 53
2.3 Statistical Interpretation of Quantum Mechanics 60
2.4 Further Development of the Statistical Interpretation: The Mean-Value Formula 71
2.5 Time Evolution of Wavefunctions and Superposition States 77
2.6 Self-Consistency of the Statistical Interpretation and the Mathematical Structure of Quantum Mechanics 95
2.7 Summary: Quantum Mechanics in a Nutshell 103
3 The Uncertainty Principle 107
3.1 Introduction 107
3.2 The Position–Momentum Uncertainty Principle 108
3.3 The Time–Energy Uncertainty Principle 114
3.4 The Uncertainty Principle in the Classical Limit 118
3.5 General Investigation of the Uncertainty Principle 119
Part II Simple Quantum Systems 127
4 Square Potentials. I: Discrete Spectrum—Bound States 129
4.1 Introduction 129
4.2 Particle in a One-Dimensional Box: The Infinite Potential Well 132
4.3 The Square Potential Well 140
5 Square Potentials. II: Continuous Spectrum—Scattering States 149
5.1 Introduction 149
5.2 The Square Potential Step: Reflection and Transmission 150
5.3 Rectangular Potential Barrier: Tunneling Effect 156
6 The Harmonic Oscillator 167
6.1 Introduction 167
6.2 Solution of the Schrödinger Equation 169
6.3 Discussion of the Results 177
6.4 A Plausible Question: Can We Use the Polynomial Method to Solve Potentials Other than the Harmonic Oscillator? 187
7 The Polynomial Method: Systematic Theory and Applications 191
7.1 Introduction: The Power-Series Method 191
7.2 Sufficient Conditions for the Existence of Polynomial Solutions: Bidimensional Equations 194
7.3 The Polynomial Method in Action: Exact Solution of the Kratzer and Morse Potentials 197
7.4 Mathematical Afterword 202
8 The Hydrogen Atom. I: Spherically Symmetric Solutions 207
8.1 Introduction 207
8.2 Solving the Schrödinger Equation for the Spherically Symmetric Eigenfunctions 209
8.3 Discussion of the Results 217
8.4 What Is the Electron Doing in the Hydrogen Atom after All? A First Discussion on the Basic Questions of Quantum Mechanics 226
9 The Hydrogen Atom. II: Solutions with Angular Dependence 231
9.1 Introduction 231
9.2 The Schrödinger Equation in an Arbitrary Central Potential: Separation of Variables 232
9.3 The Hydrogen Atom 246
10 Atoms in a Magnetic Field and the Emergence of Spin 267
10.1 Introduction 267
10.2 Atomic Electrons as Microscopic Magnets: Magnetic Moment and Angular Momentum 270
10.3 The Zeeman Effect and the Evidence for the Existence of Spin 274
10.4 The Stern–Gerlach Experiment: Unequivocal Experimental Confirmation of the Existence of Spin 278
10.5 What is Spin? 284
10.6 Time Evolution of Spin in a Magnetic Field 292
10.7 Total Angular Momentum of Atoms: Addition of Angular Momenta 295
11 Identical Particles and the Pauli Principle 305
11.1 Introduction 305
11.2 The Principle of Indistinguishability of Identical Particles in Quantum Mechanics 305
11.3 Indistinguishability of Identical Particles and the Pauli Principle 306
11.4 The Role of Spin: Complete Formulation of the Pauli Principle 307
11.5 The Pauli Exclusion Principle 310
11.6 Which Particles Are Fermions and Which Are Bosons 314
11.7 Exchange Degeneracy: The Problem and Its Solution 317
Part III Quantum Mechanics in Action: The Structure of Matter 321
12 Atoms: The Periodic Table of the Elements 323
12.1 Introduction 323
12.2 Arrangement of Energy Levels in Many-Electron Atoms: The Screening Effect 324
12.3 Quantum Mechanical Explanation of the Periodic Table: The "Small Periodic Table" 327
12.4 Approximate Calculations in Atoms: Perturbation Theory and the Variational Method 341
13 Molecules. I: Elementary Theory of the Chemical Bond 351
13.1 Introduction 351
13.2 The Double-Well Model of Chemical Bonding 352
13.3 Examples of Simple Molecules 360
13.4 Molecular Spectra 377
14 Molecules. II: The Chemistry of Carbon 393
14.1 Introduction 393
14.2 Hybridization: The First Basic Deviation from the Elementary Theory of the Chemical Bond 393
14.3 Delocalization: The Second Basic Deviation from the Elementary Theory of the Chemical Bond 414
15 Solids: Conductors, Semiconductors, Insulators 439
15.1 Introduction 439
15.2 Periodicity and Band Structure 439
15.3 Band Structure and the "Mystery of Conductivity." Conductors, Semiconductors, Insulators 441
15.4 Crystal Momentum, Effective Mass, and Electron Mobility 447
15.5 Fermi Energy and Density of States 453
16 Matter and Light: The Interaction of Atoms with Electromagnetic Radiation 469
16.1 Introduction 469
16.2 The Four Fundamental Processes: Resonance, Scattering, Ionization, and Spontaneous Emission 471
16.3 Quantitative Description of the Fundamental Processes: Transition Rate, Effective Cross Section, Mean Free Path 473
16.4 Matter and Light in Resonance. I: Theory 478
16.5 Matter and Light in Resonance. II: The Laser 487
16.6 Spontaneous Emission 494
16.7 Theory of Time-dependent Perturbations: Fermi's Rule 499
16.8 The Light Itself: Polarized Photons and Their Quantum Mechanical Description 511
Appendix 519
Bibliography 523
Index 527
