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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
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
L
2
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
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Guide
Cover
Table of Contents
Preface
Begin Reading
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, .
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 (dashed line) and (dotted) shown by the shaded area. (Both functions were assumed to be real here.)
Figure 6.2 Relation of two states (dashed) to the eigenfunctions (solid) of the operator representing the measurement .
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 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−
x
Al
x
As/GaAs/Ga
1−
x
Al
x
As 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 and dotted lines to 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 1/2
b
units) for different
E
/
V
0
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 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 , shown above the pictures. Color online.
Figure 11.3 The , and -orbitals 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 , 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
Essential Quantum Mechanics for Electrical Engineers
Peter Deák
Author
Prof. Peter Deák
University of Bremen
Bremen Center for Computational Materials Science
TAB-Gebäude
Am Fallturm 1
28359 Bremen
Germany
Cover
Background figure - “Qiwen” (Shutterstock.com); diode - “coddie” (Depositphotos.com)
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Print ISBN: 978-3-527-41355-3
ePDF ISBN: 978-3-527-80581-5
ePub ISBN: 978-3-527-80583-9
Mobi ISBN: 978-3-527-80584-6
Cover Design Bluesea Design, McLeese Lake, Canada
For my children and grandchildren.
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
Owners of a printed copy can download color figures with the help of the QR code below
http://www.wiley-vch.de/de?option=com_eshop&view=product&isbn=9783527413553
Chapter 1Introduction: Classical Physics and the Physics of Information Technology
This chapter…
describes the view of classical physics about matter. The knowledge developed from these concepts has led to the first industrial revolution; however, it is not sufficient to explain many of the present technologies. The need for a substantial extension of physics is demonstrated by following the development of lighting technology.
1.1 The Perception of Matter in Classical Physics: Particles and Waves
The task of physics is the description of the state and motion of matter in a mathematical form, which allows quantitative predictions based on known initial conditions. Mathematical relationships are established for simplified and idealized model systems. Classical physics considers two basic forms of matter: bodies and radiation, characterized by mass m and energy E, respectively. The special relativity theory of Einstein (see Section 1.9) has established that these two forms of matter can be mutually transformed into each other. In nuclear fusion or fission, for example, part of the initial mass will be converted into electromagnetic (EM) radiation (in the full spectral range from heat to X-rays), while energetic EM radiation can produce electron–positron pairs. The equivalence of mass and energy is expressed by . Still, the models used for the two forms of matter are quite different.
In classical physics, radiation is a wave in the ideally elastic continuum of the infinite EM field. Waves are characterized by their (angular) frequency ω and wave number k. These quantities are not independent, and the so-called dispersion relation between them, , determines the phase velocity f and group velocity g of the wave (see Sections 1.5 and 1.6). The energy of the wave is , where E0 is the amplitude of the EM wave.
In contrast to the continuous EM field, bodies consist of discrete particles. The fundamental building blocks are the elementary particles1 listed in Table 1.1. The model of classical physics for particles is the point mass: a geometrical point (with no extension in space) containing all the mass of the particle. It has been found that the center of mass of an extended body is moving in such a way as if all the mass was carried by it, and all the forces were acting on it. Therefore, the concept of the point mass can even be applied for extended bodies. The point mass can be characterized by its position in space (r) and by its velocity (), both of which can be accurately determined as functions of time. These kinematic quantities are then used to define the dynamic quantities, momentum p, angular momentum L, and kinetic energy T (see Section A.3).
Table 1.1 The elementary particles
Particles
First generation
Second generation
Third generation
Quarks
Up (u)
Charm (C)
Top (t)
Down (d)
Strange (S)
Bottom (b)
Leptons
Electron (e)
Muon (μ)
Tau (τ)
e-Neutrino
μ-Neutrino
τ-Neutrino
The laws and equations of classical physics are formulated for point-mass-like particles and for waves in an infinite medium.
1.2 Axioms of Classical Physics
The motion of interacting point masses can be described by the help of the four Newtonian axioms (see Section 1.2), which allow the writing down of an equation of motion for each point mass. Unfortunately, this system of equations can only be solved if the number of point masses is small or if we can assume that the distance between them is constant (rigid bodies). If the number of particles is high and the interaction between them is weak, a model of noninteracting particles (ideal gas) can be applied, and the system can be described by thermodynamic state variables. The changes in these are governed by the four laws of thermodynamics and by the equation of state. Actually, the state variables can be expressed by the Newtonian dynamic quantities, and the equation of state, as well as the four laws, can be derived from the Newtonian axioms with the help of the statistical physics and the kinetic gas theory (Figure 1.1).
Figure 1.1 Models and axioms of classical physics.
The behavior of the EM field is described by the four axioms of Maxwell's field theory (see Section 1.6). Far away from charges, these give rise to a wave equation, the solutions of which are the EM waves, traveling with the speed of light. The propagation of a local change in the field strength E can be given by the wave function E(r,t). The wave front is defined by the neighboring points in space where E has the same phase. Each point of the wave front is the source of a secondary elementary wave, and the superposition of the latter explains the well-known wave effects of refraction and diffraction.
Elastic and plastic (deformable) bodies (solids and fluids) contain a huge number of interacting particles, and neither the model of rigid bodies nor the model of the ideal gas can be applied. Instead, a continuum model can be used by assuming a continuous mass distribution, neglecting the corpuscular nature of the body. In the case of elastic bodies, the Newtonian equation for an infinitesimal volume of the continuum leads to a wave equation. The solutions are mechanical waves, corresponding to the propagation of local changes in the position (vibrations). The concepts and mathematics of mechanical and EM waves are quite similar.
Figure 1.2 Scientists who were instrumental in the development of the point mass concept for particles.
The pictures are taken from the public domain image collection of http://de.wikipedia.org
1.3 Status and Effect of Classical Physics by the End of the Nineteenth Century
As we have seen in the previous subsection, classical physics contains two relatively independent parts: mechanics (from which also the thermodynamics can be derived) and electrodynamics (including optics).2 Particles in classical mechanics are described by the concept of the point mass. In a conservative force field, where the potential energy V(x,t) can be defined, the position of the point mass can be obtained from the Newtonian equation of motion:
Historically (see Figure 1.2), the concept of the point mass has evolved, among others, from
the mathematical formulation of the observed regularities in the planetary motions (by, e.g.,
J. Kepler
);
the mathematical formulation of the experimentally observed motion of bodies on earth (by, e.g.,
G. Gallilei
);
the establishment of the axioms of mechanics (by
I. Newton
).
The concept of elementary particles, as the building blocks of a body, could later be confirmed in electrical measurements, too (e.g., by E. Millikan, who has shown that the electric charge of an oil droplet, floating in the field of a capacitor, can only be changed by discrete amounts, corresponding to the elementary charge, i.e., to the charge of an electron). The application of the principles of mechanics and thermodynamics around the end of the nineteenth century has led to the invention and optimization of structures and machines such as the ones shown in Figure 1.3.
Figure 1.3 Application of mechanics and thermodynamics around the end of the nineteenth century.
(a: The picture of the Eiffel tower was taken by the author. b: Power station, reproduced with permission of Daniel Hinze. c: Old locomotive, reproduced with permission of Herbert Schambach. d: The picture of the airplane was taken from the public domain of http://en.wikipedia.org.)
Figure 1.4 Scientists who were instrumental in the development of the concept of electromagnetic waves.
(The public domain of http://en.wikipedia.org.)
The interpretation of light as a wave in the EM field is based on the wave equation, derived from Maxwell's axioms:
where ψ is either the electric or the magnetic field and f the phase velocity (c in vacuum).
Historically (see Figure 1.4), the concept of the EM waves has evolved, among others, from
the mathematical formulation of the laws of diffraction (e.g., by
A. J. Fresnel
);
the mathematical formulation of the experimentally observed relations of electromagnetics (e.g., by
M. Faraday
);
the establishment of the axioms of the EM field (by
J. C. Maxwell
).
The concept of the EM waves could later be confirmed in experiments (e.g., by H. Hertz, who could generate and detect radio waves), which are the basis of today's telecommunication technology. The application of the principles of electrodynamics (and wave optics) around the end of the nineteenth century has led to the invention of electrical lighting, the first forms of electrical data transfer and of “exotic rays” (see Figure 1.5).
Figure 1.5
