Essential Quantum Mechanics for Electrical Engineers

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 xiii1 Introduction: Classical Physics and the Physics of Information Technology 11.1 The Perception of Matter in Classical Physics: Particles and Waves 11.2 Axioms of Classical Physics 21.3 Status and Effect of Classical Physics by the End of the Nineteenth Century 31.4 Physics Background of the High-Tech Era 61.5 Developments in Physics Reflected by the Development of Lighting Technology 71.6 The Demand for Physics in Electrical Engineering and Informatics: Today and Tomorrow 111.7 Questions and Exercises 132 Blackbody Radiation: The Physics of the Light Bulb and of the Pyrometer 152.1 Electromagnetic Radiation of Heated Bodies 152.2 Electromagnetic Field in Equilibrium with theWalls of a Metal Box 172.3 Determination of the Average Energy per Degree of Freedom. Planck’s Law 182.4 Practical Applications of Planck’s Law for the Blackbody Radiation 192.5 Significance of Planck’s Law for the Physics 212.6 Questions and Exercises 223 Photons: The Physics of Lasers 253.1 The Photoelectric Effect 253.2 Practical Applications of the Photoelectric Effect (Photocell, Solar Cell, Chemical Analysis) 273.3 The Compton Effect 283.4 The Photon Hypothesis of Einstein 293.5 Planck’s Law and the Photons. Stimulated Emission 303.6 The Laser 313.7 Questions and Exercises 344 Electrons: The Physics of the Discharge Lamps 374.1 Fluorescent Lamp 374.2 Franck–Hertz Experiment 384.3 Bohr’s Model of the Hydrogen Atom: Energy Quantization 404.4 Practical Consequences of the Energy Quantization for Discharge Lamps 424.5 The de Broglie Hypothesis 454.6 The Davisson–Germer Experiment 464.7 Wave–Particle Dualism of the Electron 474.8 Questions and Exercises 485 The Particle Concept of Quantum Mechanics 515.1 Particles andWaves in Classical Physics 515.2 Double-Slit Experiment with a Single Electron 535.3 The Born–Jordan Interpretation of the ElectronWave 555.4 Heisenberg’s Uncertainty Principle 555.5 Particle Concept of Quantum Mechanics 565.6 The Scale Dependence of Physics 575.7 Toward a New Physics 585.8 The Significance of ElectronWaves for Electrical Engineering 595.9 Displaying ElectronWaves 605.10 Questions and Exercises 616 Measurement in Quantum Mechanics. Postulates 1–3 636.1 Physical Restrictions for theWave Function of an Electron 646.2 Mathematical Definitions and Laws Related to theWave6.3 Mathematical Representation of the Measurement by6.4 Mathematical Definitions and Laws Related to Operators 676.5 Measurement in Quantum Mechanics 687 Observables in Quantum Mechanics. Postulates 4 and 5. The Relation of Classical and Quantum Mechanics 757.1 The Canonical Commutation Relations of Heisenberg 757.2 The Choice of Operators by Schr̈odinger 767.3 Vector Operator of the Angular Momentum 777.4 Energy Operators and the Schr̈odinger Equation 787.5 Time Evolution of Observables 797.6 The EhrenfestTheorem 817.7 Questions and Exercises 828 Quantum Mechanical States 858.1 Eigenstates of Position 858.2 Eigenstates of Momentum 878.3 Eigenstates of Energy – Stationary States 888.4 Free Motion 908.5 Bound States 928.6 Questions and Exercises 949 The QuantumWell: the Basis of Modern Light-Emitting Diodes (LEDs) 979.1 Quantum-Well LEDs 979.2 Energy Eigenvalues in a Finite QuantumWell 999.3 Applications in LEDs and in Detectors 1039.4 Stationary States in a Finite QuantumWell 1039.5 The Infinite QuantumWell 1049.6 Comparison to a Classical Particle in a Box 1069.7 Questions and Exercises 10710 The Tunnel Effect and Its Role in Electronics 10910.1 The Scanning Tunneling Microscope 10910.2 Electron at a Potential Barrier 11010.3 Field Emission, Leakage Currents, Electrical Breakdown, Flash Memories 11310.4 Resonant Tunneling, Quantum Field Effect Transistor, Quantum-Cascade Lasers 11710.5 Questions and Exercises 12211 The Hydrogen Atom. Quantum Numbers. Electron Spin 12511.1 Eigenstates of Lz 12611.2 Eigenstates of L2 12611.3 Energy Eigenstates of an Electron in the Hydrogen Atom 12911.4 Angular Momentum of the Electrons.The Spin 13411.5 Questions and Exercises 13612 Quantum Mechanics of Many-Body Systems (Postulates 6 and 7). The Chemical Properties of Atoms. Quantum Information Processing 13912.1 The Wave Function of a System of Identical Particles 13912.2 The Pauli Principle 14012.3 Independent Electron Approximation (One-Electron Approximation) 14212.4 Atoms with Several Electrons 14512.5 The Chemical Properties of Atoms 14512.6 The Periodic System of Elements 14712.7 Significance of the Superposition States for the Future of Electronics and Informatics 14812.8 Questions and Exercises 151A Important Formulas of Classical Physics 153A.1 Basic Concepts 153A.1.1 The PointMass 153A.1.2 Frame of Reference 153A.1.3 The Path 153A.1.4 Kinematics 153A.2 Newton’s Axioms 154A.3 Conservation Laws 155A.4 Examples 156A.5 Waves in an Elastic Medium 157A.6 Wave Optics 159A.7 Equilibrium Energy Distribution among Many Particles 160A.8 Complementary Variables 162A.9 Special Relativity Theory 162B Important Mathematical Formulas 165B.1 Numbers 165B.2 Calculus 166B.3 Operators 167B.4 Differential Equations 168B.5 Vectors and Matrices 169C List of Abbreviations 171Solutions 177List of Figures 189Index 197