Essential Quantum Mechanics for Electrical

Quantum mechanics (QM) is latently present in the life of electrical engineers already, since the hardware of todays information technology - from electrical data processing, through interconversion of electronic and optical information, to data storage and visualization - works on QM principles. New developments in micro- and opto-electronics and the advent of quantum information processing will soon make the active understanding of QM unavoidable for engineers, too. Unfortunately, the principles of QM can only be formulated mathematically, so even introductory books on the subject are mostly rather abstract. This book, written mainly for BSc students, tries to help the reader by showing "QM in action", demonstrating its surprising effects directly in applications, like lighting technology, lasers, photo- and solar cells, flash memories and quantum bits.

While the axioms and basic concepts of quantum mechanics are introduced without compromises, the math is kept at a level which is required from electrical engineers anyhow. Computational work is spared by the use of Applets which also visualize the results. Among the host of other didactic features are learning objectives, chapter summaries, self-testing questions, and problems with solutions, while two appendices summarize the knowledge in classical physics and mathematics which is needed for this book.

Peter Deak is currently Professor of Theoretical Semiconductor Physics at the University of Bremen, Germany, and head of the Electronic Materials Group in the Bremen Center of Computational Materials Science. After obtaining his PhD at the Eotvos University of Budapest, Hungary, and post-doctoral positions at SUNY, Albany, the Max Planck Institute for Solid State Research in Stuttgart and the University of Kaiserslautern, Germany, he obtained a tenure as professor of surface physics at the Budapest Institute of Technology and Economics in 1993. He relocated to Germany in 2003 where he took up his current position in Bremen. Peter Deak has more than 25 years of experience in teaching physics to undergraduates of electrical engineering and informatics.

Preface xiii

1 Introduction: Classical Physics and the Physics of Information Technology 1

1.1 The Perception of Matter in Classical Physics: Particles and Waves 1

1.2 Axioms of Classical Physics 2

1.3 Status and Effect of Classical Physics by the End of the Nineteenth Century 3

1.4 Physics Background of the High-Tech Era 6

1.5 Developments in Physics Reflected by the Development of Lighting Technology 7

1.6 The Demand for Physics in Electrical Engineering and Informatics: Today and Tomorrow 11

1.7 Questions and Exercises 13

2 Blackbody Radiation: The Physics of the Light Bulb and of the Pyrometer 15

2.1 Electromagnetic Radiation of Heated Bodies 15

2.2 Electromagnetic Field in Equilibrium with theWalls of a Metal Box 17

2.3 Determination of the Average Energy per Degree of Freedom. Planck’s Law 18

2.4 Practical Applications of Planck’s Law for the Blackbody Radiation 19

2.5 Significance of Planck’s Law for the Physics 21

2.6 Questions and Exercises 22

3 Photons: The Physics of Lasers 25

3.1 The Photoelectric Effect 25

3.2 Practical Applications of the Photoelectric Effect (Photocell, Solar Cell, Chemical Analysis) 27

3.3 The Compton Effect 28

3.4 The Photon Hypothesis of Einstein 29

3.5 Planck’s Law and the Photons. Stimulated Emission 30

3.6 The Laser 31

3.7 Questions and Exercises 34

4 Electrons: The Physics of the Discharge Lamps 37

4.1 Fluorescent Lamp 37

4.2 Franck–Hertz Experiment 38

4.3 Bohr’s Model of the Hydrogen Atom: Energy Quantization 40

4.4 Practical Consequences of the Energy Quantization for Discharge Lamps 42

4.5 The de Broglie Hypothesis 45

4.6 The Davisson–Germer Experiment 46

4.7 Wave–Particle Dualism of the Electron 47

4.8 Questions and Exercises 48

5 The Particle Concept of Quantum Mechanics 51

5.1 Particles andWaves in Classical Physics 51

5.2 Double-Slit Experiment with a Single Electron 53

5.3 The Born–Jordan Interpretation of the ElectronWave 55

5.4 Heisenberg’s Uncertainty Principle 55

5.5 Particle Concept of Quantum Mechanics 56

5.6 The Scale Dependence of Physics 57

5.7 Toward a New Physics 58

5.8 The Significance of ElectronWaves for Electrical Engineering 59

5.9 Displaying ElectronWaves 60

5.10 Questions and Exercises 61

6 Measurement in Quantum Mechanics. Postulates 1–3 63

6.1 Physical Restrictions for theWave Function of an Electron 64

6.2 Mathematical Definitions and Laws Related to theWave

6.3 Mathematical Representation of the Measurement by

6.4 Mathematical Definitions and Laws Related to Operators 67

6.5 Measurement in Quantum Mechanics 68

7 Observables in Quantum Mechanics. Postulates 4 and 5. The Relation of Classical and Quantum Mechanics 75

7.1 The Canonical Commutation Relations of Heisenberg 75

7.2 The Choice of Operators by Schr̈odinger 76

7.3 Vector Operator of the Angular Momentum 77

7.4 Energy Operators and the Schr̈odinger Equation 78

7.5 Time Evolution of Observables 79

7.6 The EhrenfestTheorem 81

7.7 Questions and Exercises 82

8 Quantum Mechanical States 85

8.1 Eigenstates of Position 85

8.2 Eigenstates of Momentum 87

8.3 Eigenstates of Energy – Stationary States 88

8.4 Free Motion 90

8.5 Bound States 92

8.6 Questions and Exercises 94

9 The QuantumWell: the Basis of Modern Light-Emitting Diodes (LEDs) 97

9.1 Quantum-Well LEDs 97

9.2 Energy Eigenvalues in a Finite QuantumWell 99

9.3 Applications in LEDs and in Detectors 103

9.4 Stationary States in a Finite QuantumWell 103

9.5 The Infinite QuantumWell 104

9.6 Comparison to a Classical Particle in a Box 106

9.7 Questions and Exercises 107

10 The Tunnel Effect and Its Role in Electronics 109

10.1 The Scanning Tunneling Microscope 109

10.2 Electron at a Potential Barrier 110

10.3 Field Emission, Leakage Currents, Electrical Breakdown, Flash Memories 113

10.4 Resonant Tunneling, Quantum Field Effect Transistor, Quantum-Cascade Lasers 117

10.5 Questions and Exercises 122

11 The Hydrogen Atom. Quantum Numbers. Electron Spin 125

11.1 Eigenstates of Lz 126

11.2 Eigenstates of L2 126

11.3 Energy Eigenstates of an Electron in the Hydrogen Atom 129

11.4 Angular Momentum of the Electrons.The Spin 134

11.5 Questions and Exercises 136

12 Quantum Mechanics of Many-Body Systems (Postulates 6 and 7). The Chemical Properties of Atoms. Quantum Information Processing 139

12.1 The Wave Function of a System of Identical Particles 139

12.2 The Pauli Principle 140

12.3 Independent Electron Approximation (One-Electron Approximation) 142

12.4 Atoms with Several Electrons 145

12.5 The Chemical Properties of Atoms 145

12.6 The Periodic System of Elements 147

12.7 Significance of the Superposition States for the Future of Electronics and Informatics 148

12.8 Questions and Exercises 151

A Important Formulas of Classical Physics 153

A.1 Basic Concepts 153

A.1.1 The PointMass 153

A.1.2 Frame of Reference 153

A.1.3 The Path 153

A.1.4 Kinematics 153

A.2 Newton’s Axioms 154

A.3 Conservation Laws 155

A.4 Examples 156

A.5 Waves in an Elastic Medium 157

A.6 Wave Optics 159

A.7 Equilibrium Energy Distribution among Many Particles 160

A.8 Complementary Variables 162

A.9 Special Relativity Theory 162

B Important Mathematical Formulas 165

B.1 Numbers 165

B.2 Calculus 166

B.3 Operators 167

B.4 Differential Equations 168

B.5 Vectors and Matrices 169

C List of Abbreviations 171

Solutions 177

List of Figures 189

Index 197

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Essential Quantum Mechanics for Electrical Engineers

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