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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This is an introductory textbook tailored for a one semester course on quantum mechanics at a technically oriented school. It covers fundamental quantum mechanics from an application's perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors. The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds. Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts. The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.
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Seitenzahl: 492
Veröffentlichungsjahr: 2016
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Table of Contents
Cover
Related Titles
Title Page
Copyright
Dedication
Preface
Chapter 1: Review of Classical Theories
1.1 Harmonic Oscillator
1.2 Boltzmann Distribution Function
1.3 Maxwell's Equations and EM Waves
Problems
Suggested Readings
Chapter 2: Milestones Leading to Quantum Mechanics
2.1 Blackbody Radiation and Quantum of Energy
2.2 Photoelectric Effect and Photon
2.3 Compton Scattering
2.4 de Broglie Wavelength and Duality of Matter
2.5 Hydrogen Atom and Spectroscopy
Problems
Suggested Readings
Chapter 3: Schrödinger Wave Equation
3.1 Operator Algebra and Basic Postulates
3.2 Eigenequation, Eigenfuntion and Eigenvalue
3.3 Properties of Eigenfunctions
3.4 Commutation Relation and Conjugate Variables
3.5 Uncertainty Relation
Problems
Suggested Readings
Chapter 4: Bound States in Quantum Well and Wire
4.1 Electrons in Solids
4.2 1D, 2D, and 3D Densities of States
4.3 Particle in Quantum Well
4.4 Quantum Well and Wire
Problems
Suggested Readings
Chapter 5: Scattering and Tunneling of 1D Particle
5.1 Scattering at the Step Potential
5.2 Scattering from a Quantum Well
5.3 Tunneling
5.4 The Applications of Tunneling
Problems
Suggested Readings
Chapter 6: Energy Bands in Solids
6.1 Bloch Wavefunction in Kronig–Penney Potential
6.2
E–k
Dispersion and Energy Bands
6.3 The Motion of Electrons in Energy Bands
6.4 Energy Bands and Resonant Tunneling
Problems
Suggested Readings
Chapter 7: The Quantum Treatment of Harmonic Oscillator
7.1 Energy Eigenfunction and Energy Quantization
7.2 The Properties of Eigenfunctions
7.3 HO in Linearly Superposed State
7.4 The Operator Treatment of HO
Problems
Suggested Readings
Chapter 8: Schrödinger Treatment of Hydrogen Atom
8.1 Angular Momentum Operators
8.2 Spherical Harmonics and Spatial Quantization
8.3 The H-Atom and Electron–Proton Interaction
Problems
Suggested Readings
Chapter 9: The Perturbation Theory
9.1 Time-Independent Perturbation Theory
9.2 Time-Dependent Perturbation Theory
Problems
Suggested Readings
Chapter 10: System of Identical Particles and Electron Spin
10.1 Electron Spin
10.2 Two-Electron System
10.3 Interaction of Electron Spin with Magnetic Field
10.4 Electron Paramagnetic Resonance
Problems
Suggested Readings
Chapter 11: Molecules and Chemical Bonds
11.1 Ionized Hydrogen Molecule
11.2 H
2
Molecule and Heitler-London Theory
11.3 Ionic Bond
11.4 van der Waals Attraction
11.5 Polyatomic Molecules and Hybridized Orbitals
Problems
Suggested Readings
Chapter 12: Molecular Spectra
12.1 Theoretical Background
12.2 Rotational and Vibrational Spectra of Diatomic Molecule
12.3 Nuclear Spin and Hyperfine Interaction
12.4 Nuclear Magnetic Resonance (NMR)
Problems
Suggested Readings
Chapter 13: Atom–Field Interaction
13.1 Atom–Field Interaction: Semiclassical Treatment
13.2 Driven Two-Level Atom and Atom Dipole
13.3 Atom–Field Interaction: Quantum Treatment
Problems
Suggested Readings
Chapter 14: The Interaction of EM Waves with an Optical Media
14.1 Attenuation, Amplification, and Dispersion of Waves
14.2 Atomic Susceptibility
14.3 Laser Device
Problems
Suggested Readings
Chapter 15: Semiconductor Statistics
15.1 Quantum Statistics
15.2 Carrier Concentration in Intrinsic Semiconductor
15.3 Carrier Densities in Extrinsic Semiconductors
Problems
Suggested Readings
Chapter 16: Carrier Transport in Semiconductors
16.1 Quantum Description of Transport Coefficients
16.2 Equilibrium and Nonequilibrium
16.3 Generation and Recombination Currents
Problems
Suggested Readings
Chapter 17: P–N Junction Diode: I–V Behavior and Device Physics
17.1 The p–n Junction in Equilibrium
17.2 The p–n Junction under Bias
17.3 Ideal Diode I–V Behavior
17.4 Nonideal I–V Behavior
Problems
Suggested Readings
Chapter 18: P–N Junction Diode: Applications
18.1 Optical Absorption
18.2 Photodiode
18.3 Solar Cell
18.4 LED and LD
Problems
Suggested Readings
Chapter 19: Field-Effect Transistors
19.1 The Modeling of MOSFET
I–V
19.2 Silicon Nanowire Field-Effect Transistor
19.3 Tunneling NWFET as Low-Power Device
Problems
Suggested Readings
Chapter 20: The Application and Novel Kinds of FETs
20.1 Nonvolatile Flash EEPROM Cell
20.2 Semiconductor Solar Cells
20.3 Biosensor
20.4 Spin Field-Effect Transistor
20.5 Spin Qubits and Quantum Computing
Problems
Suggested Readings
Solutions
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Index
Important Physical Numbers and Quantities
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 3.1
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12
Figure 6.1
Figure 6.2
Figure 6.4
Figure 6.3
Figure 6.5
Figure 6.7
Figure 7.1
Figure 7.2
Figure 7.3
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 9.1
Figure 9.2
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 13.1
Figure 13.2
Figure 13.3
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 16.1
Figure 16.2
Figure 16.3
Figure 16.4
Figure 16.5
Figure 16.6
Figure 16.7
Figure 16.8
Figure 16.9
Figure 17.1
Figure 17.2
Figure 17.3
Figure 17.4
Figure 17.5
Figure 17.6
Figure 17.7
Figure 18.1
Figure 18.2
Figure 18.3
Figure 18.4
Figure 18.5
Figure 18.6
Figure 18.7
Figure 19.1
Figure 19.2
Figure 19.3
Figure 19.4
Figure 19.5
Figure 19.6
Figure 19.7
Figure 19.8
Figure 19.9
Figure 19.10
Figure 20.1
Figure 20.2
Figure 20.3
Figure 20.4
Figure 20.5
Figure 20.6
Figure 20.7
Figure 20.8
Figure 20.9
List of Tables
Table 8.1
Table 8.2
Table 10.1
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DaeMann Kim
Introductory Quantum Mechanics for Applied Nanotechnology
Author
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Korea Inst. f. Advanced Study
Cheongnyangni 2-dong
130-722 Seoul
South Korea
Cover
© Istockphoto/kynny
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Preface
The multidisciplinary science education has been prompted by the rapid advancement and utilization of IT/BT/NT, and the quantum mechanics is the basic science supporting the technologies. It further provides the platform on which to bridge different disciplines in science and engineering. This introductory textbook is intended for the undergraduate seniors and beginning graduate students and is focused on the application and multidisciplinary aspects of the quantum mechanics.
The applications have been chosen primarily from the semiconductor and optoelectronic devices to make the discussion practical. The p-n junction diode is first singled out for the discussion as the simplest solid state switch and also as photodiode, light-emitting and laser diodes and solar cells. Moreover, the field effect transistors are treated in some detail. The well-known theory of MOSFET is first compactly presented to serve as the general background for considering other kinds of novel FETs such as nanowire and spin field-effect transistors. The working principles of these devices are treated from a unified standpoint of the equilibrium and nonequilibrium statistics and device physics in conjunction with the quantum mechanical concepts. Additionally, these FETs as the nonvolatile memory cells, biosensor, and solar cells are highlighted. As an extension of the discussion of the spin FET the quantum computing is briefly touched upon.
The organization of the book is as follows. The classical and statistical mechanics and the electromagnetic fields are compactly summarized as a general background. After a short visit to the milestones leading to quantum mechanics, the Schrödinger equation is applied immediately to problems of practical interests, involving the quantum wells and subbands, 1D, 2D, and 3D densities of states. In particular, the tunneling and its applications are highlighted. Two key bound systems are treated in some detail. Specifically, the harmonic oscillator is analyzed based on the quantum mechanical and operator treatments. In addition, the hydrogen atom is considered as the simplest atomic system and as an essential ingredient for analyzing the atomic spectroscopy, multielectron atoms, paramagnetic electron resonance and molecules.
The chemical bond for the molecular formation is included in the discussion list. In particular, the molecular spectroscopy is treated as an extension of the atomic spectroscopy by utilizing the time-independent perturbation theory and focused on the rotational and vibrational motions of diatomic molecules. The nuclear spin, hyperfine structure, and nuclear magnetic resonance for molecular imaging are briefly introduced. Moreover, the interaction of light with matter is highlighted, based on the time-dependent perturbation theory, and the operation principle of the laser is elucidated. Finally, the semiconductor statistics and the transport of the charge carriers are discussed as an essential background for modeling the semiconductor devices. An effort has been expended to make the presentation and discussion brief and clear by simplifying the mathematics and by making use of the analogies existing between different dynamic systems.
The contents of this book have evolved from the courses offered in the Department of Electrical and Computer engineering, Rice University, Houston, TX., USA; POSTECH, Pohang, Korea; and the College of Engineering, Seoul National University, Seoul, Korea. The active and enthusiastic participation of the attending students made it a joyful experience to teach the courses. My thanks are due to those students. I would also like to express my sincere thanks to Miss You-Na Hwang for her tireless cooperation in preparing the figures for the book. Finally, it is my pleasure and honor to express my heartfelt gratitude to Professor Willis E. Lamb, whose courses on quantum mechanics and laser physics were most inspiring.
Seoul, KoreaDae Mann Kim
Chapter 1Review of Classical Theories
A compact review of classical theories is presented, including the classical and statistical mechanics and electromagnetism. These theories are inherently intertwined with quantum mechanics and provide the general background from which to understand the quantum mechanics in a proper perspective.
1.1 Harmonic Oscillator
The harmonic oscillator (HO) is one of the simplest, yet ubiquitous dynamical systems appearing in a variety of physical and chemical systems such as electromagnetic waves and molecules. The HO is a particle attached to a spring, executing oscillatory motion. When the spring is compressed or stretched, the spring provides a restoring force for putting the particle back to the equilibrium position (Figure 1.1). In the process, an oscillatory motion ensues, and the motion represents a variety of important natural phenomena such as molecular vibrations and electromagnetic waves.
Figure 1.1 The harmonic oscillator, a particle of mass m attached to a spring with the spring constant k (a); the potential energy of HO (b); a diatomic molecule as represented by two atoms coupled via an effective spring constant (c).
Newton's equation of motion of the HO reads as
where m is the mass of the oscillator, x the displacement from the equilibrium position, and k the spring constant. The double dots denote the second-order differentiation with respect to time, and −kx is Hook's restoring force. The equation can be put into a form
where ω is the characteristic frequency. Trigonometric functions, for example, , are well-known solutions of Eq. (1.2). When the oscillator is pulled by x0 and gently released, for instance, the displacement x(t) and the velocity v(t) are given by
and x(t), v(t) oscillate in time in quadrature (Figure 1.2) with the period .
Figure 1.2 The displacement x, velocity v, and kinetic K and potential V energies versus ωt, all scaled with respective maximum values. The total energy is constant in time, and HO is a conservative system.
The potential energy of the HO is obtained by integrating the work done for displacing the HO from the equilibrium position to x against the restoring force:
The total energy is often denoted by Hamiltonian H and is expressed in terms of the linear momentum px and the displacement x as
Given H, Hamilton's equations of motion read as
The pair of equations in (Eq. (1.6)), when combined, reduces to Newton's equation of motion, and the variables x, px are known as canonically conjugate variables. The essence of classical mechanics is to solve the equation of motion and to precisely specify the position and momentum of a particle or a system of particles.
1.2 Boltzmann Distribution Function
The properties of macroscopic quantities are derived from the dynamics of an ensemble of microscopic objects such as electrons, holes, atoms, and molecules. Statistical mechanics describes such an ensemble of particles by means of the distribution function, f (r, v, t). The function represents the probability of finding the particles in the phase space volume element drdv at r, v, and t. Thus, when multiplied by density n of the particle f (r, v, t) drdv represents the number of particles in the volume element at
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