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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Chapter 1 Introduction: 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 soluti...
Table of contents
Cover
Title Page
Copyright
Dedication
Table of Contents
Preface
Chapter 1: Introduction: Classical Physics and the Physics of Information Technology
Chapter 2: Blackbody Radiation: The Physics of the Light Bulb and of the Pyrometer
Chapter 3: Photons: The Physics of Lasers
Chapter 4: Electrons: The Physics of the Discharge Lamps
Chapter 5: The Particle Concept of Quantum Mechanics
Chapter 6: Measurement in Quantum Mechanics. Postulates 1–3
Chapter 7: Observables in Quantum Mechanics. Postulates 4 and 5. The Relation of Classical and Quantum Mechanics
Chapter 8: Quantum Mechanical States
Chapter 9: The Quantum Well: the Basis of Modern Light-Emitting Diodes (LEDs)
Chapter 10: The Tunnel Effect and Its Role in Electronics
Chapter 11: The Hydrogen Atom. Quantum Numbers. Electron Spin
Chapter 12: Quantum Mechanics of Many-Body Systems (Postulates 6 and 7). The Chemical Properties of Atoms. Quantum Information Processing
Appendix A: Important Formulas of Classical Physics
