An Introduction to Quantum Physics

Ein umfassendes Lehrbuch der Quantenphysik und Chemie sowie der Struktur von Materie. Eignet sich für Anfänger und Fortgeschrittene und bietet zusätzlich Online-Übungen zur Überprüfung des Lehrstoffes, Laborübungen mit Mathematica sowie ein komplettes Lösungshandbuch.

Auteur

Stefanos Trachanas is an educator, author, and publisher. For over 35 years he has taught most of the core undergraduate courses at the Physics Department of the University of Crete. His books on quantum mechanics and differential equations are used as primary textbooks in most Greek University Departments of Physics, Chemistry, Materials Science, and Engineering. He is a cofounder of Crete University Press, which he led as Director from 1984 until his retirement in 2013.
His awards include an honorary doctorate from the University of Crete, the Xanthopoulos-Pnevmatikos national award for excellence in academic teaching, and the Knight Commander of the Order of Phoenix, bestowed by the President of Greece.

Manolis Antonoyiannakis is an Associate Editor and Bibliostatistics Analyst at the American Physical Society. He is also an Adjunct Associate Research Scientist at the Department of Applied Physics & Applied Mathematics at Columbia University, USA. He received his Master's degree from the University of Illinois at Urbana-Champaign, USA, and his PhD from Imperial College London, UK.
His editorial experience in the Physical Review journals stimulated his interest in statistical, sociological, and historical aspects of peer review, but also in scientometrics and information science. He is currently developing data science tools to analyze scientific publishing and enhance research assessment.

Leonidas Tsetseris is an Associate Professor at the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens, Greece. He obtained his Master's and PhD degrees in physics from the University of Illinois at Urbana-Champaign, USA.
His research expertise is on computational condensed matter physics and materials science, particularly quantum-mechanical studies on emerging materials. He has taught a variety of university physics courses, including classical mechanics, electromagnetism, quantum mechanics, and solid state physics.

Résumé

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.

Contenu

Foreword xix

Preface xxiii

Editors' Note xxvii

Part I Fundamental Principles 1

1 The Principle of WaveParticle Duality: An Overview 3

1.1 Introduction 3

1.2 The Principle of WaveParticle Duality of Light 4

1.2.1 The Photoelectric Effect 4

1.2.2 The Compton Effect 7

1.2.3 A Note on Units 10

1.3 The Principle of WaveParticle Duality of Matter 11

1.3.1 From Frequency Quantization in Classical Waves to Energy Quantization in Matter Waves: The Most Important General Consequence of WaveParticle Duality of Matter 12

1.3.2 The Problem of Atomic Stability under Collisions 13

1.3.3 The Problem of Energy Scales: Why Are Atomic Energies on the Order of eV, While Nuclear Energies Are on the Order of MeV? 15

1.3.4 The Stability of Atoms and Molecules Against External Electromagnetic Radiation 17

1.3.5 The Problem of Length Scales: Why Are Atomic Sizes on the Order of Angstroms, While Nuclear Sizes Are on the Order of Fermis? 19

1.3.6 The Stability of Atoms Against Their Own Radiation: Probabilistic Interpretation of Matter Waves 21

1.3.7 How Do Atoms Radiate after All? Quantum Jumps from Higher to Lower Energy States and Atomic Spectra 22

1.3.8 Quantized Energies and Atomic Spectra: The Case of Hydrogen 25

1.3.9 Correct and Incorrect Pictures for the Motion of Electrons in Atoms: Revisiting the Case of Hydrogen 25

1.3.10 The Fine Structure Constant and Numerical Calculations in Bohr's Theory 29

1.3.11 Numerical Calculations with Matter Waves: Practical Formulas and Physical Applications 31

1.3.12 A Direct Confirmation of the Existence of Matter Waves: The DavissonGermer Experiment 33

1.3.13 The Double-Slit Experiment: Collapse of the Wavefunction Upon Measurement 34

1.4 Dimensional Analysis and Quantum Physics 41

1.4.1 The Fundamental Theorem and a Simple Application 41

1.4.2 Blackbody Radiation Using Dimensional Analysis 44

1.4.3 The Hydrogen Atom Using Dimensional Analysis 47

2 The Schrödinger Equation and Its Statistical Interpretation 53

2.1 Introduction 53

2.2 The Schrödinger Equation 53

2.2.1 The Schrödinger Equation for Free Particles 54

2.2.2 The Schrödinger Equation in an External Potential 57

2.2.3 Mathematical Intermission I: Linear Operators 58

2.3 Statistical Interpretation of Quantum Mechanics 60

2.3.1 The ParticleWave Contradiction in Classical Mechanics 60

2.3.2 Statistical Interpretation 61

2.3.3 Why Did We Choose P(x) = |𝜓(x)|

2 as the Probability Density? 62

2.3.4 Mathematical Intermission II: Basic Statistical Concepts 63

2.3.4.1 Mean Value 63

2.3.4.2 Standard Deviation (or Uncertainty) 65

2.3.5 Position Measurements: Mean Value and Uncertainty 67

2.4 Further Development of the Statistical Interpretation: The Mean-Value Formula 71

2.4.1 The General Formula for the Mean Value 71

2.4.2 The General Formula for Uncertainty 73

2.5 Time Evolution of Wavefunctions and Superposition States 77

2.5.1 Setting the Stage 77

2.5.2 Solving the Schrödinger Equation. Separation of Variables 78

2.5.3 The Time-Independent Schrödinger Equation as an Eigenvalue Equation: Zero-Uncertainty States and Superposition States 81

2.5.4 Energy Quantization for Confined Motion: A Fundamental General Consequence of Schrödinger's Equation 85

2.5.5 The Role of Measurement in Quantum Mechanics: Collapse of the Wavefunction Upon Measurement 86

2.5.6 Measurable Consequences of Time Evolution: Stationary and Nonstationary States 91

2.6 Self-Consistency of the Statistical Interpretation and the Mathematical Structure of Quantum Mechanics 95

2.6.1 Hermitian Operators 95

2.6.2 Conservation of Probability 98

2.6.3 Inner Product and Orthogonality 99

2.6.4 Matrix Representation of Quantum Mechanical Operators 101

2.7 Summary: Quantum Mechanics in a Nutshell 103

3 The Uncertainty Principle 107

3.1 Introduction 107 &...