Table of Contents

Cover

Title Page

Dedication

Preface

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

1.1 The Perception of Matter in Classical Physics: Particles and Waves
1.2 Axioms of Classical Physics
1.3 Status and Effect of Classical Physics by the End of the Nineteenth Century
1.4 Physics Background of the High-Tech Era
1.5 Developments in Physics Reflected by the Development of Lighting Technology
1.6 The Demand for Physics in Electrical Engineering and Informatics: Today and Tomorrow
1.7 Questions and Exercises

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

2.1 Electromagnetic Radiation of Heated Bodies
2.2 Electromagnetic Field in Equilibrium with the Walls of a Metal Box
2.3 Determination of the Average Energy per Degree of Freedom. Planck's Law
2.4 Practical Applications of Planck's Law for the Blackbody Radiation
2.5 Significance of Planck's Law for the Physics
2.6 Questions and Exercises

Chapter 3: Photons: The Physics of Lasers

3.1 The Photoelectric Effect
3.2 Practical Applications of the Photoelectric Effect (Photocell, Solar Cell, Chemical Analysis)
3.3 The Compton Effect
3.4 The Photon Hypothesis of Einstein
3.5 Planck's Law and the Photons. Stimulated Emission
3.6 The Laser
3.7 Questions and Exercises

Chapter 4: Electrons: The Physics of the Discharge Lamps

4.1 Fluorescent Lamp
4.2 Franck–Hertz Experiment
4.3 Bohr's Model of the Hydrogen Atom: Energy Quantization
4.4 Practical Consequences of the Energy Quantization for Discharge Lamps
4.5 The de Broglie Hypothesis
4.6 The Davisson–Germer Experiment
4.7 Wave–Particle Dualism of the Electron
4.8 Questions and Exercises

Chapter 5: The Particle Concept of Quantum Mechanics

5.1 Particles and Waves in Classical Physics
5.2 Double-Slit Experiment with a Single Electron
5.3 The Born–Jordan Interpretation of the Electron Wave
5.4 Heisenberg's Uncertainty Principle
5.5 Particle Concept of Quantum Mechanics
5.6 The Scale Dependence of Physics
5.7 Toward a New Physics
5.8 The Significance of Electron Waves for Electrical Engineering
5.9 Displaying Electron Waves
5.10 Questions and Exercises
Reference

Chapter 6: Measurement in Quantum Mechanics. Postulates 1–3

6.1 Physical Restrictions for the Wave Function of an Electron
6.2 Mathematical Definitions and Laws Related to the Wave Function
6.3 Mathematical Representation of the Measurement by Operators
6.4 Mathematical Definitions and Laws Related to Operators
6.5 Measurement in Quantum Mechanics
6.6 Questions and Exercises

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

7.1 The Canonical Commutation Relations of Heisenberg
7.2 The Choice of Operators by Schrödinger
7.3 Vector Operator of the Angular Momentum
7.4 Energy Operators and the Schrödinger Equation
7.5 Time Evolution of Observables
7.6 The Ehrenfest Theorem

Chapter 8: Quantum Mechanical States

8.1 Eigenstates of Position
8.2 Eigenstates of Momentum
8.3 Eigenstates of Energy – Stationary States
8.4 Free Motion
8.5 Bound States
8.6 Questions and Exercises

Chapter 9: The Quantum Well: the Basis of Modern Light-Emitting Diodes (LEDs)

9.1 Quantum-Well LEDs
9.2 Energy Eigenvalues in a Finite Quantum Well
9.3 Applications in LEDs and in Detectors
9.4 Stationary States in a Finite Quantum Well
9.5 The Infinite Quantum Well
9.6 Comparison to a Classical Particle in a Box
9.7 Questions and Exercises

Chapter 10: The Tunnel Effect and Its Role in Electronics

10.1 The Scanning Tunneling Microscope
10.2 Electron at a Potential Barrier
10.3 Field Emission, Leakage Currents, Electrical Breakdown, Flash Memories
10.4 Resonant Tunneling, Quantum Field Effect Transistor, Quantum-Cascade Lasers
10.5 Questions and Exercises

Chapter 11: The Hydrogen Atom. Quantum Numbers. Electron Spin

11.1 Eigenstates of L_z
11.2 Eigenstates of L²
11.3 Energy Eigenstates of an Electron in the Hydrogen Atom
11.4 Angular Momentum of the Electrons. The Spin
11.5 Questions and Exercises

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

12.1 The Wave Function of a System of Identical Particles
12.2 The Pauli Principle
12.3 Independent Electron Approximation (One-Electron Approximation)
12.4 Atoms with Several Electrons
12.5 The Chemical Properties of Atoms
12.6 The Periodic System of Elements
12.7 Significance of the Superposition States for the Future of Electronics and Informatics
12.8 Questions and Exercises
References

Appendix A: Important Formulas of Classical Physics

A.1 Basic Concepts
A.2 Newton's Axioms
A.3 Conservation Laws
A.4 Examples
A.5 Waves in an Elastic Medium
A.6 Wave Optics
A.7 Equilibrium Energy Distribution among Many Particles
A.8 Complementary Variables
A.9 Special Relativity Theory

Appendix B: Important Mathematical Formulas

B.1 Numbers
B.2 Calculus
B.3 Operators
B.4 Differential Equations
B.5 Vectors and Matrices

Appendix C: List of Abbreviations

Solutions

Index

End User License Agreement

List of Illustrations

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

Figure 1.1 Models and axioms of classical physics.
Figure 1.2 Scientists who were instrumental in the development of the point mass concept for particles.
Figure 1.3 Application of mechanics and thermodynamics around the end of the nineteenth century.
Figure 1.4 Scientists who were instrumental in the development of the concept of electromagnetic waves.
Figure 1.5 Application of electrodynamics and optics around the end of the nineteenth century.
Figure 1.6 The hardware of information technology. Color online.
Figure 1.7 Stages in the development of lighting technology: the light bulb, compact fluorescence lamp (discharge lamp), and the LED lamp.
Figure 1.8 Spectral energy distribution of heat radiation. The black solid lines show (somewhat idealized) experimental curves, while the red dashed line shows the prediction of classical physics at T = 2000 K. A dotted line shows the shift of the wavelength with maximal energy as the temperature increases. Color online.
Figure 1.9 Schematic view of a fluorescent tube.
Figure 1.10 Light-emitting diodes and laser pointers of different colors, as well as the schematic (nonproportional) view of a white LED.

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

Figure 2.1 Spectrum of the sun and of a tungsten-halogen lamp (a) and contactless temperature measurement by a pyrometer (b).
Figure 2.2 Modeling of an ideal radiator. Color online.
Figure 2.3 Spectral distribution of the energy density of the EM field in equilibrium with an ideal blackbody, according to Planck and according to Rayleigh and Jeans, at different temperatures.
Figure 2.4 Phototopic (solid line) and scotopic (dashed line) spectral luminous efficiency, $c02-math-037$ .

Chapter 3: Photons: The Physics of Lasers

Figure 3.1 The photoelectric effect. Color online.
Figure 3.2 Energy scheme of the photoelectric effect in a metal (a) and of the photovoltaic effect in a semiconductor (b).
Figure 3.3 The Compton effect as photon scattering by an electron.
Figure 3.4 Light absorption and emission by transitions between two states of energy.
Figure 3.5 Light amplification by stimulated emission.
Figure 3.6 Components of a laser.
Figure 3.7 Transitions in two-level (a), three-level (b), and four-level (c) systems. The laser transition is shown in red. Color online.
Figure 3.8 Laser types: diode laser (a), ruby laser (b), and He–Ne laser (c). Color online.

Chapter 4: Electrons: The Physics of the Discharge Lamps

Figure 4.1 Structure of a discharge lamp.
Figure 4.2 The Franck–Hertz experiment.
Figure 4.3 Measuring the emission of a hydrogen plasma. The spectrum is shown at the bottom. Color online.
Figure 4.4 Bohr's model of the hydrogen atom.
Figure 4.5 Low- (a) and high- (b) pressure sodium lamps. Color online.
Figure 4.6 High-pressure metal-halide lamp and its spectrum Color online.
Figure 4.7 Scheme of the light emission by phosphor. Color online.
Figure 4.8 Comparison of lamp spectra with that of the sun measured at sea level. (Color online.)
Figure 4.9 Stationary wave along a circle.
Figure 4.10 (A) Schematic depiction of the Davisson–Germer diffraction experiment with electrons. (B) Diffraction pattern obtained by an X-ray (a) and by electrons (b).

Chapter 5: The Particle Concept of Quantum Mechanics

Figure 5.1 The two main parts of classical physics.
Figure 5.2 Concepts of classical physics.
Figure 5.3 The duality problem of light and bodies.
Figure 5.4 Expected outcome of a double-slit experiment (b) with a single electron according to the duality principle: classical point mass (a) and classical wave (c).
Figure 5.5 Actual outcome of the double-slit experiment with single electrons detected on a CCD screen. In (a–c) snapshots are shown after an increasing number of electron shots. The experiment was performed by Tonomura et al. [1].
Figure 5.6 The point-mass concept of classical particles, expressed in terms of the probability of observing a given position and momentum. According to Eq. (5.3), this concept cannot be applied to an electron.
Figure 5.7 Possible states of an electron, expressed in terms of the probability of observing a given position and momentum.
Figure 5.8 The “Parable of the parabola people.”
Figure 5.9 I–V characteristics of the semiconductor GaAs, used, for example, in Gunn diodes.
Figure 5.10 Schematic of a scanning tunneling microscope and the current image of an electron captured as standing wave within a fence of 48 iron atoms on a copper surface. Color online.

Chapter 6: Measurement in Quantum Mechanics. Postulates 1–3

Figure 6.1 The meaning of the scalar product of $c06-math-072$ (dashed line) and $c06-math-073$ (dotted) shown by the shaded area. (Both functions were assumed to be real here.)
Figure 6.2 Relation of two states $c06-math-086$ (dashed) to the eigenfunctions $c06-math-087$ (solid) of the operator representing the measurement $c06-math-088$ .

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

Figure 7.1 The angular momentum in polar coordinates.
Figure 7.2 Comparison of the potential energy V (solid line) with the localization of the particle (shaded area).

Chapter 8: Quantum Mechanical States

Figure 8.1 The generalized function of Eq. (8.2), displayed for increasing integration limits a. The Dirac delta function corresponds to a = ∞. Color online.
Figure 8.2 Probability density for measuring the position x_i.
Figure 8.3 Delocalization of the wave packet describing a freely moving electron. Color online.
Figure 8.4 Impermissible (E) and allowed $c08-math-080$ bound states. Color online.
Figure 8.5

Chapter 9: The Quantum Well: the Basis of Modern Light-Emitting Diodes (LEDs)

Figure 9.1 Schematic representation of a simple light-emitting diode. Electrons (blue) in the conduction band are negative, the holes (red) in the valence band are positive charge carriers. Color online.
Figure 9.2 Electron and hole potentials (upper and lower thick line, respectively) in a Ga_1−xAl_xAs/GaAs/Ga_1−xAl_xAs semiconductor heterostructure sandwiched in the z direction.
Figure 9.3 The one-dimensional potential well.
Figure 9.4 Graphic solution for the Schrödinger equation of the quantum well. Color online. Dashed lines correspond to $c09-math-046$ and dotted lines to $c09-math-047$ functions.
Figure 9.5 Dependence of the allowed energy levels on the height and width of the quantum well. Color online.
Figure 9.6 Electron and hole levels in the QW-LED.
Figure 9.7 Energy eigenstates, with the corresponding energy levels used as x-axis: (a) finite and (b) infinite QW. Color online.

Chapter 10: The Tunnel Effect and Its Role in Electronics

Figure 10.1 Schematic representation of a scanning tunneling microscope. Color online.
Figure 10.2 One-dimensional potential wall.
Figure 10.3 Electron transmission at a potential wall (cf. Eq. (10.6)).
Figure 10.4 Dependence of the electron transmission T on the width of the potential wall d (in 1/2b units) for different E/V₀ ratios. Color online.
Figure 10.5 Wave packet at the potential wall (dashed lines in the middle).
Figure 10.6 Potential in the vicinity of the cathode in field emission.
Figure 10.7 Scheme of a MOS-FET. Color online. (The semiconductor has different electrical properties in the regions marked n and p.)
Figure 10.8 Electric breakdown of an insulator due to the tunnel effect. The triangular potential wall, arising after the voltage is applied, is depicted similarly to Figure 10.6. Color online.
Figure 10.9 Penetration of harmonic waves, with energy increasing in 0.05 eV steps, into a quantum well (width 2 nm, height 1.5 eV, wall thickness 0.2 nm). Dashed lines show the position of the potential walls. (Snapshots from the applet https://phet.colorado.edu/en/simulation/quantum-tunneling).
Figure 10.10 Schematic view of a quantum field effect transistor. Color online.
Figure 10.11 Operation principle and structure of a cascade laser (reproduces by the kind permission of Conrad Holton) and a commercial tunable cascade laser (Block engineering's Mini-QCL® https://www.laserfocusworld.com).
Figure 10.12 One-dimensional potential trap.
Figure 10.13 Resonant tunneling into a potential trap.
Figure 10.14 Scheme of an FG-MOS used in solid-state storage devices (flash memories).

Chapter 11: The Hydrogen Atom. Quantum Numbers. Electron Spin

Figure 11.1 Isosurface representation of the spherical harmonics. From top to bottom: the s-, the three p-, the five d-, and the seven f-orbitals. Blue means positive and yellow negative isovalues of the same magnitude. Color online.
Figure 11.2 The 1s-, 2s-, and 3s-orbitals $c011-math-101$ of the electron in a hydrogen atom. Positive values are shown in yellow, negatives in blue, and the color intensity indicates the variation of the magnitude, as given by the radial function $c011-math-102$ , shown above the pictures. Color online.
Figure 11.3 The $c011-math-103$ , and $c011-math-104$ -orbitals $c011-math-105$ of the electron in a hydrogen atom. Positive values are shown in yellow, negatives in blue, and the color intensity indicates the variation of the magnitude, as given by the radial function $c011-math-106$ , shown above the pictures. Color online.
Figure 11.4 Overview of the electron orbitals in the hydrogen atom for Used under Creative commons license CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/.)
Figure 11.5 The radial probability distribution of the electron in various states in the hydrogen atom.
Figure 11.6 Possible orientations of the electron spin. (The end point of the vector must be on the upper or the lower circle.)
Figure 11.7 The discrete energy levels of one electron in the field of Z protons. The radial parts of the orbitals are depicted using the corresponding levels as r-axis. Color online.
Figure 11.8 Two electron states in the hydrogen atom, depicted by their radial part using the energy levels in the Coulomb potential as abscissa.

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

Figure 12.1 Splitting and occupation of the energy levels in an atom with many electrons. Color online.
Figure 12.2 Interaction between the electrons of two atoms. For details, see the text. Color online.
Figure 12.3 Occupation sequence of the atomic orbitals with periodically repeated s-, p-, d-, and f-character for the valence shell.
Figure 12.4 Periodic system of the elements.
Figure 12.5 International road map for semiconductors (Moore's law).
Figure 12.6 Entanglement between the spins of two nitrogen + vacancy defects by a photon in a diamond crystal.

List of Tables

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

Table 1.1 The elementary particles

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

Table 2.1 Characteristics of the incandescent lamps

Chapter 3: Photons: The Physics of Lasers

Table 3.1 Characteristics of different laser types

Chapter 4: Electrons: The Physics of the Discharge Lamps

Table 4.1 Characteristics of discharge lamps for interior lighting

Background figure - “Qiwen” (Shutterstock.com); diode - “coddie” (Depositphotos.com)

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Preface

My motivation for writing this book was the expected effect of nanotechnology on engineering, which will surely and significantly enhance the demand for the knowledge of quantum mechanics (QM). Although present-day micro- and optoelectronics can, to a degree, be understood using semiclassical models, this situation is going to change soon. The limits of development in the traditional (twentieth century) hardware have almost been reached. The upcoming devices – where switching happens at the level of single electrons, tunnel effects are actively utilized, and superposition states of electrons are used as qubits – are based on phenomena that cannot be grasped even approximately without the conceptual understanding of QM. Most students graduating in electrical engineering in the coming years will definitely be confronted in their professional career with the paradigm shift induced by the new technologies of the quantum world. This explains why the teaching of QM should begin early.

Although teaching QM to students of electrical engineering (and informatics) at the undergraduate level is becoming more and more widespread, there are hardly any textbooks written specifically for such courses. Typical books on QM are not well suited for engineers because of the excessive use of mathematics and because of the very abstract way of treatment with little or no applications relevant to them. QM books written for electrical engineers are usually either resorting to heuristics or aim at the band theory of solids (to be able to describe semiconductor applications), the latter being well beyond the possibilities provided by a bachelor curriculum. Based on my 25 years of experience in teaching QM for undergraduate students of electrical engineering and informatics, I have attempted to write a textbook, adjusted to their knowledge level and interests, which can be the basis of a two hours a week, one semester course.

From the viewpoint of electrical engineering, QM is primarily the physics of electrons. Its knowledge enables us to use them for information processing, storage, and display, as well as for lighting and energy production. Our organs of perception cannot register individual electrons, so we cannot really imagine what they are really like. As Richard Feynman has formulated it, the electron is not an object (what we can see or hold) but a concept, which can only be formulated mathematically. Accordingly, QM can only be formulated and interpreted mathematically, and this seems to be, at the first sight to undergraduates in electrical engineering, rather difficult to digest and of little practical interest. However, information technology is an important part of the trade, and the physics necessary to understand the hardware of electronic data processing and the conversion between electronic and electromagnetic information in data storage, transfer, and display has become indispensable. The majority of the graduates in electrical engineering and informatics will primarily be interested in system integration and algorithms, but optimal efficiency can only be achieved if they have an at least conceptual understanding about the working of the devices to be integrated and programmed. In addition, QM has changed our perception of reality very much, allowing a much deeper understanding of nature. Therefore, it should be part of the education of anybody striving for a bachelor degree in science and technology.

This book was specifically written for undergraduates of electrical engineering and shows the interlocking between the development of QM and the hardware of lighting technology, opto-, and microelectronics, as well as quantum information processing. I have attempted to demonstrate the surprising claims of basic QM in direct applications. The “Introduction” summarizes the basic concepts of classical physics and points out some of its failures, based on phenomena connected to lighting technology. These (blackbody radiation in the light bulb, emission spectrum of the gas fill, and cathode emission in discharge lamps) are analyzed in detail in Chapters 2–4, based on experiments which are famous in physics. It is shown that a surprising but rather controversial first explanation of the results could be provided in terms of the wave–particle duality principle. The use of that by Einstein led later to the discovery of the laser (which is also described). Chapter 5 goes beyond the duality principle and explains the particle concept of the QM and its consequences for electrical engineering (e.g., negative differential resistivity). Chapters 6–8 introduce the mathematical construction used for describing the state of a particle and to predict its properties. In Chapters 9 and 10, two examples of using this framework are shown (potential well and tunneling through a potential barrier), with applications, among others, in light-emitting diodes, infrared detectors, quantum cascade lasers, Zener diodes, and flash memories. The scanning tunneling microscope is, of course, explained and also the leakage currents in integrated circuits and the electric breakdown of insulators. Finally, in Chapters 11 and 12, some consequences of the QM for the chemical properties of atoms and for other many-electron systems (such as semiconductors) are depicted, giving also a brief insight into the potential hardware for quantum information processing. In Appendices A and B, the knowledge in classical physics and mathematics is summarized, which is a prerequisite to read the book. (It is strongly recommended to work through these appendices first.)

This book attempts to choose a middle course between abstract mathematics and applications. On the one hand, basic concepts and principles of the QM are introduced in the necessary mathematical formulation, but the mathematics is kept as simple as possible. Only those tools of advanced mathematics are used, which have to be learned in the electronic engineering curriculum anyhow, and even they are used to treat specific cases relevant for applications. Engineers usually prefer ready-made formulas over mathematical derivation. However, since the internal logic of QM is actually in the derivations, the most important ones are shown in this book – but only as footnotes. Chapters 9 and 10 are the two exceptions from this rule, where practically applicable formulas can be derived in elementary steps, helping the reader to gain a deeper understanding of specific cases. In addition, knowing very well that the targeted readers are mostly not too mathematics oriented, the book exploits the possibilities of multimedia: besides numerous figures and pictures, video clips and applets, accessible on the Internet, are used intensively. Application of QM often requires serious efforts with numerical calculations, but applets can ease the burden of that, allowing quick visualization of trends and easier cognition of graphically displayed information.

Finally, it should be noted that QM has raised many philosophical, epistemological questions. As far as possible, these have been swept under the carpet in this book, and – to use a philosophical term – a rather positivistic representation was chosen. Since this book was written for engineers, prediction of practical results should take precedence over philosophical interpretation. In addition, it is probably better to get a simplified but applicable picture, which later can be refined, than being bogged down right at the beginning with interpretational controversies.

I would like to express my gratitude to the people who have helped me to complete this book: Dr Bálint Aradi and Dr Michael Lorke, who have read and corrected the original German version, and Prof. Japie Engelbrecht who did the same with this English one.

Bremen 2016

Peter Deák