The second edition of Modern Physics for Scientists and Engineers is intended for a first course in modern physics. Beginning with a brief and focused account of the historical events leading to the formulation of modern quantum theory, later chapters delve into the underlying physics. Streamlined content, chapters on semiconductors, Dirac equation and quantum field theory, as well as a robust pedagogy and ancillary package, including an accompanying website with computer applets, assist students in learning the essential material. The applets provide a realistic description of the energy levels and wave functions of electrons in atoms and crystals. The Hartree-Fock and ABINIT applets are valuable tools for studying the properties of atoms and semiconductors.
- Develops modern quantum mechanical ideas systematically and uses these ideas consistently throughout the book
- Carefully considers fundamental subjects such as transition probabilities, crystal structure, reciprocal lattices, and Bloch theorem which are fundamental to any treatment of lasers and semiconductor devices
- Clarifies each important concept through the use of a simple example and often an illustration
- Features expanded exercises and problems at the end of each chapter
- Offers multiple appendices to provide quick-reference for students
John Morrison received a BS degree in Physics from University of Santa
Clara in California. During his undergraduate years, he majored in English,
Philosophy, and Physics and served as the editor of the campus literary magazine,
the Owl. Enrolling at Johns Hopkins University in Baltimore, Maryland,
he received a PhD degree in theoretical Physics and moved on to postdoctoral
research at Argonne National Laboratory where he was a member of the Heavy
Atom Group.
He then went to Sweden where he received a grant from the Swedish Research
Council to build up a research group in theoretical atomic physics at
Chalmers Technical University in Goteborg, Sweden. Working together with
Ingvar Lindgren, he taught a graduate level-course in theoretical atomic physics
for a number of years. Their teaching lead to the publication of the monograph,
Atomic Many-Body Theory, which rst appeared as Volume 13 of the Springer
Series on Chemical Physics. The second edition of this book has become a
Springer classic.
Returning to the United States, John Morrison obtained a position in the
Department of Physics and Astronomy at University of Louisville where he has
taught courses in elementary physics, astronomy, modern physics, and quantum
mechanics. In recent years, he has traveled extensively in Latin America and
the Middle East maintaining contacts with scientists and mathematicians at the
Hebrew University in Jerusalem and the Technion University in Haifa. During
the Fall semester of 2009, he taught a course on computational physics at Birzeit
University near Ramallah on the West Bank, and he has recruited Palestinian
students for the graduate program in physics at University of Louisville. He
speaks English, Swedish, and Spanish, and he is currently studying Arabic and
Hebrew.
The second edition of Modern Physics for Scientists and Engineers is intended for a first course in modern physics. Beginning with a brief and focused account of the historical events leading to the formulation of modern quantum theory, later chapters delve into the underlying physics. Streamlined content, chapters on semiconductors, Dirac equation and quantum field theory, as well as a robust pedagogy and ancillary package, including an accompanying website with computer applets, assist students in learning the essential material. The applets provide a realistic description of the energy levels and wave functions of electrons in atoms and crystals. The Hartree-Fock and ABINIT applets are valuable tools for studying the properties of atoms and semiconductors. Develops modern quantum mechanical ideas systematically and uses these ideas consistently throughout the book Carefully considers fundamental subjects such as transition probabilities, crystal structure, reciprocal lattices, and Bloch theorem which are fundamental to any treatment of lasers and semiconductor devices Clarifies each important concept through the use of a simple example and often an illustration Features expanded exercises and problems at the end of each chapter Offers multiple appendices to provide quick-reference for students
Front Cover 1
Modern Physics: for Scientists and Engineers 4
Copyright 5
Dedication 6
Contents 8
Preface 12
This New Edition 12
New Features 12
The Nature of the Book 13
Acknowledgments 16
Introduction 18
I.1. The Concepts of Particles and Waves 18
I.1.1. The Variables of a Moving Particle 18
I.1.2. Elementary Properties of Waves 20
I.1.3. Interference and Diffraction Phenomena 27
I.2. An Overview of Quantum Physics 30
Basic Equations 35
Summary 36
Suggestions for Further Reading 37
Questions 37
Problems 37
Chapter 1: The Wave-Particle Duality 40
1.1. The Particle Model of Light 40
1.1.1. The Photoelectric Effect 40
1.1.2. The Absorption and Emission of Light by Atoms 43
1.1.3. The Compton Effect 49
1.2. The Wave Model of Radiation and Matter 51
1.2.1. X-ray Scattering 51
1.2.2. Electron Waves 52
Suggestions for Further Reading 54
Basic Equations 54
Photoelectric Effect 54
Emission and Absorption of Radiation by Atoms 55
Wave Properties of Radiation and Matter 55
Summary 55
Questions 55
Problems 56
Chapter 2: The Schrödinger Wave Equation 58
2.1. The Wave Equation 58
2.2. Probabilities and Average Values 62
2.3. The Finite Potential Well 65
2.4. The Simple Harmonic Oscillator 69
2.4.1. The Schrödinger Equation for the Oscillator 71
2.5. Time Evolution of the Wave Function 72
Suggestion for Further Reading 75
Basic Equations 75
The Wave Equation 75
Solutions of Schrödinger Time-Independent Equation 75
Time Evolution of Wave Function 76
Summary 76
Questions 76
Problems 77
Chapter 3: Operators and Waves 80
3.1. Observables, Operators, and Eigenvalues 81
3.2. A Closer Look at the Finite Well 84
3.3. Electron Scattering 88
3.3.1. Scattering from a Potential Step 88
3.3.2. Barrier Penetration and Tunneling 92
3.4. The Heisenberg Uncertainty Principle 95
3.4.1. Wave Packets and the Uncertainty Principle 96
3.4.2. Average Value of the Momentum and the Energy 99
Suggestion for Further Reading 100
Basic Equations 100
Observables, Operators, and Eigenvalues 100
Electron Scattering 100
The Heisenberg Uncertainty Principle 101
Summary 101
Questions 102
Problems 102
Chapter 4: The Hydrogen Atom 104
4.1. The Gross Structure of Hydrogen 104
4.1.1. The Schrödinger Equation in Three Dimensions 104
4.1.2. The Energy Levels of Hydrogen 106
4.1.3. The Wave Functions of Hydrogen 107
4.1.4. Probabilities and Average Values in Three Dimensions 110
4.1.5. The Intrinsic Spin of the Electron 112
4.2. Radiative Transitions 113
4.2.1. The Einstein A and B Coefficients 113
4.2.2. Transition Probabilities 114
4.2.3. Selection Rules 118
4.3. The Fine Structure of Hydrogen 119
4.3.1. The Magnetic Moment of the Electron 119
4.3.2. The Stern-Gerlach Experiment 122
4.3.3. The Spin of the Electron 123
4.3.4. The Addition of Angular Momentum 124
4.3.5. * The Fine Structure 125
4.3.6. * The Zeeman Effect 127
Suggestion For Further Reading 129
Basic Equations 129
Wave Function for Hydrogen 129
Probabilities and Average Values 129
Transition Probabilities 129
Selection Rules 129
The Fine Structure of Hydrogen 130
Summary 130
Questions 131
Problems 131
Chapter 5: Many-Electron Atoms 134
5.1. The Independent-Particle Model 134
5.1.1. Antisymmetric Wave Functions and the Pauli Exclusion Principle 135
5.1.2. The Central-Field Approximation 136
5.2. Shell Structure and the Periodic Table 137
5.3. The LS Term Energies 139
5.4. Configurations of Two Electrons 139
5.4.1. Configurations of Equivalent Electrons 140
5.4.2. Configurations of Two Nonequivalent Electrons 142
5.5. The Hartree-Fock Method 143
5.5.1. The Hartree-Fock Applet 144
5.5.2. The Size of Atoms and the Strength of Their Interactions 147
Suggestion for Further Reading 152
Basic Equations 152
Definition of Atomic Units 152
Atomic Unit of Distance 152
Atomic Unit of Energy 152
Summary 152
Questions 153
Problems 153
Chapter 6: The Emergence of Masers and Lasers 156
6.1. Radiative Transitions 156
6.2. Laser Amplification 157
6.3. Laser Cooling 162
6.4. * Magneto-Optical Traps 162
Suggestions for Further Reading 165
Basic Equations 166
Hamiltonian of Outer Electron in the Magnetic Field of Nucleus 166
Total Angular Momentum of Electron and Nucleus 166
The z-Component of Magnetic Moment of Outer Electron 166
The Energy of the Outer Electron Due to the Magnetic Field B 166
Summary 166
Questions 166
Problems 167
Chapter 7: Statistical Physics 168
7.1. The Nature of Statistical Laws 168
7.2. An Ideal Gas 171
7.3. Applications of Maxwell-Boltzmann Statistics 173
7.3.1. Maxwell Distribution of the Speeds of Gas Particles 173
7.3.2. Black-Body Radiation 179
7.4. Entropy and the Laws of Thermodynamics 184
7.4.1. The Four Laws of Thermodynamics 186
7.5. A Perfect Quantum Gas 188
7.6. Bose-Einstein Condensation 192
7.7. Free-Electron Theory of Metals 194
Suggestions for Further Reading 199
Basic Equations 200
Maxwell-Boltzmann Statistics 200
Applications of Maxwell-Boltzmann Statistics 200
Entropy and the Laws of Thermodynamics 200
Quantum Statistics 201
Free-Electron Theory of Metals 201
Summary 201
Questions 202
Problems 203
Chapter 8: Electronic Structure of Solids 206
8.1. Introduction 206
8.2. The Bravais Lattice 207
8.3. Additional Crystal Structures 211
8.3.1. The Diamond Structure 211
8.3.2. The hcp Structure 211
8.3.3. The Sodium Chloride Structure 212
8.4. The Reciprocal Lattice 213
8.5. Lattice Planes 216
8.6. Bloch's Theorem 220
8.7. Diffraction of Electrons by an Ideal Crystal 224
8.8. The Bandgap 226
8.9. Classification of Solids 228
8.9.1. The Band Picture 228
Insulators 228
Semiconductors 228
Metals 229
Graphene 229
Carbon Nanotubes 231
8.9.2. The Bond Picture 231
Covalent Bonding 232
Ionic Bonding 233
Molecular Crystals 234
Hydrogen-Bonded Crystals 234
Metals 234
Suggestions for Further Reading 235
Basic Equations 235
Bravais Lattice 235
Reciprocal Lattice 236
Bloch’s Theorem 236
Scattering of Electrons by a Crystal 236
Summary 236
Questions 237
Problems 237
Chapter 9: Charge Carriers in Semiconductors 242
9.1. Density of Charge Carriers in Semiconductors 242
9.2. Doped Crystals 245
9.3. A Few Simple Devices 246
9.3.1. The p-n Junction 247
9.3.2. Bipolar Transistors 249
9.3.3. Junction Field-Effect Transistors 250
9.3.4. MOSFETs 251
Suggestions for Further Reading 251
Summary 252
Questions 252
Chapter 10: Semiconductor Lasers 254
10.1. Motion of Electrons in a Crystal 254
10.2. Band Structure of Semiconductors 256
10.2.1. Conduction Bands 256
10.2.2. Valence Bands 257
10.2.3. Optical Transitions 257
10.3. Heterostructures 259
10.3.1. Properties of Heterostructures 259
10.3.2. Experimental Methods 260
10.3.3. Theoretical Methods 262
10.3.4. Band Engineering 263
10.4. Quantum Wells 264
10.4.1. The Finite Well 265
10.4.2. Two-Dimensional Systems 265
10.4.3. *Quantum Wells in Heterostructures 266
10.5. Quantum Barriers 268
10.5.1. Scattering from a Potential Step 268
10.5.2. T-Matrices 270
10.5.3. Scattering from More Complex Barriers 271
10.6. Reflection and Transmission of Light 274
10.6.1. Reflection and Transmission by an Interface 275
10.6.2. The Fabry-Perot Laser 277
10.7. Phenomenological Description of Diode Lasers 278
10.7.1. The Rate Equation 279
10.7.2. Well Below Threshold 281
10.7.3. The Laser Threshold 281
10.7.4. Above Threshold 282
Suggestions for Further Reading 283
Basic Equations 283
Quantum Wells 283
Potential Barriers 284
Reflection and Transmission of Light by an Interface 284
Phenomenological Description of Diode Lasers 284
Summary 285
Questions 285
Problems 286
Chapter 11: Relativity I 288
11.1. Galilean Transformations 288
11.2. The Relative Nature of Simultaneity 291
11.3. Lorentz Transformation 293
11.3.1. The Transformation Equations 293
11.3.2. Lorentz Contraction 296
11.3.3. Time Dilation 297
11.3.4. The Invariant Space-Time Interval 300
11.3.5. Addition of Velocities 301
11.3.6. The Doppler Effect 302
11.4. Space-Time Diagrams 304
11.4.1. Particle Motion 305
11.4.2. Lorentz Transformations 308
11.4.3. The Light Cone 309
11.5. Four-Vectors 310
Suggestions For Further Reading 314
Basic Equations 315
Galilean Transformations 315
The Relativistic Transformations 315
Four-Vectors 316
Summary 316
Questions 316
Problems 317
Chapter 12: Relativity II 320
12.1. Momentum and Energy 320
12.2. Conservation of Energy and Momentum 323
12.3. * The Dirac Theory of the Electron 327
12.3.1. Review of the Schrödinger Theory 327
12.3.2. The Klein-Gordon Equation 329
12.3.3. The Dirac Equation 329
12.3.4. Plane Wave Solutions of the Dirac Equation 332
12.4. * Field Quantization 335
Suggestions For Further Reading 337
Basic Equations 337
Definitions 337
The Dirac Theory of the Electron 338
Summary 339
Questions 339
Problems 340
Chapter 13: Particle Physics 342
13.1. Leptons and Quarks 342
13.2. Conservation Laws 349
13.2.1. Energy, Momentum, and Charge 349
13.2.2. Lepton Number 350
13.2.3. Baryon Number 351
13.2.4. Strangeness 353
13.2.5. Charm, Beauty, and Truth 355
13.3. Spatial Symmetries 356
13.3.1. Angular Momentum of Composite Systems 356
13.3.2. Parity 357
13.3.3. Charge Conjugation 359
13.4. Isospin and Color 361
13.4.1. Isospin 361
13.4.2. Color 367
13.5. Feynman Diagrams 369
13.5.1. Electromagnetic Interactions 370
13.5.2. Weak Interactions 371
13.5.3. Strong Interactions 373
13.6. * The Flavor and Color SU(3) Symmetries 374
13.6.1. The SU(3) Symmetry Group 375
13.6.2. The Representations of SU(3) 377
13.7. * Gauge Invariance and the Electroweak Theory 382
13.8. Spontaneous Symmetry Breaking and the Discovery of the Higgs 384
Suggestion for Further Reading 387
Basic Equations 388
Leptons and Quarks 388
Definition of Hypercharge and Isospin 388
Isospin 388
Feynman Diagrams 388
SU(3) Symmetry 388
Summary 389
Questions 389
Problems 390
Chapter 14: Nuclear Physics 392
14.1. Properties of Nuclei 392
14.1.1. Nuclear Sizes 393
14.1.2. Binding Energies 396
14.1.3. The Semi-Empirical Mass Formula 398
14.2. Decay Processes 400
14.2.1. a-Decay 401
14.2.2. The ß-Stability Valley 402
14.2.3. .-Decay 404
14.2.4. Natural Radioactivity 406
14.3. The Nuclear Shell Model 407
14.3.1. Nuclear Potential Wells 407
14.3.2. Nucleon States 408
14.3.3. Magic Numbers 410
14.3.4. The Spin-Orbit Interaction 410
14.4. Excited States of Nuclei 411
Suggestions for Further Reading 415
Basic Equations 415
Binding Energy 415
The Semi-Empirical Formula 415
Magic Numbers 415
Summary 415
Questions 416
Problems 416
Appendix A: Constants and Conversion Factors 420
Constants 420
Particle Masses 420
Conversion Factors 421
Appendix B: Atomic Masses 422
Appendix C: Introduction to MATLAB 428
Creating a Vector 428
Plotting Functions 429
Using Arrays in MATLAB 429
Using Functions in MATLAB 430
Appendix D: Solution of the Oscillator Equation 432
Appendix E. The Average Value of the Momentum 436
Appendix F. The Hartree-Fock Applet 438
Appendix G. Integrals that Arise in Statistical Physics 440
Reference 442
Further Reading 442
Index 444
Appendix AA. The Gradient and Laplacian Operators 450
The Gradient Operator 450
The Divergence of a Vector 450
The Laplacian of a Function 451
The Angular Momentum Operators 451
Appendix BB. Solution of the Schrödinger Equation in Spherical Coordinates 454
Separation of the Schrödinger Equation 454
Appendix CC. More Accurate Solutions of the Eigenvalue Problem 460
A 5-Point Finite Difference Formula 460
Appendix DD. The Angular Momentum Operators 468
Generalization of the Quantum Rules 468
Commution Relations 468
Spectrum of Eigenvalues 471
Appendix EE. The Radial Equation for Hydrogen 474
Appendix FF: Transition Probabilities for z-Polarized Light 476
Appendix GG: Transitions with x- and y-Polarized Light 480
Appendix HH: Derivation of the Distribution Laws 482
Maxwell-Boltzmann Statistics 482
Bose-Einstein Statistics 483
Fermi-Dirac Statistics 484
Appendix II: Derivation of Bloch's Theorem 486
Appendix JJ: The Band Gap 488
Appendix KK: Vector Spaces and Matrices 492
Appendix LL: Algebraic Solution of the Oscillator 496
Introduction
Every physical system can be characterized by its size and the length of time it takes for processes occurring within it to evolve. This is as true of the distribution of electrons circulating about the nucleus of an atom as it is of a chain of mountains rising up over the ages.
Modern physics is a rich field including decisive experiments conducted in the early part of the twentieth century and more recent research that has given us a deeper understanding of fundamental processes in nature. In conjunction with our growing understanding of the physical world, a burgeoning technology has led to the development of lasers, solid-state devices, and many other innovations. This book provides an introduction to the fundamental ideas of modern physics and to the various fields of contemporary physics in which discoveries and innovation are going on continuously.
I.1 The Concepts of Particles and Waves
While some of the ideas currently used to describe microscopic systems differ considerably from the ideas of classical physics, other important ideas are classical in origin. We begin this chapter by discussing the important concepts of a particle and a wave which have the same meaning in classical and modern physics. A particle is an object with a definite mass concentrated at a single location in space, while a wave is a disturbance that propagates through space. The first section of this chapter, which discusses the elementary properties of particles and waves, provides a review of some of the fundamental ideas of classical physics. Other elements of classical physics will be reviewed later in the context for which they are important. The second section of this chapter describes some of the central ideas of modern quantum physics and also discusses the size and time scales of the physical systems considered in this book.
I.1.1 The Variables of a Moving Particle
The position and velocity vectors of a particle are illustrated in Fig. I.1. The position vector r extends from the origin to the particle, while the velocity vector v points in the direction of the particle’s motion. Other variables, which are appropriate for describing a moving particle, can be defined in terms of these elementary variables.
The momentum p of the particle is equal to the product of the mass and velocity v of the particle
=mv.
We shall find that the momentum is useful for describing the motion of electrons in an extended system such as a crystal.
The motion of a particle moving about a center of force can be described using the angular momentum, which is defined to be the cross product of the position and momentum vectors
=r×p.
The cross product of two vectors is a vector having a magnitude equal to the product of the magnitudes of the two vectors times the sine of the angle between them. Denoting the angle between the momentum and position vectors by θ as in Fig. I.1, the magnitude of the angular momentum vector momentum can be written
ℓ|=|r||p|sinθ.
This expression for the angular momentum may be written more simply in terms of the distance between the line of motion of the particle and the origin, which is denoted by r0 in Fig. I.1. We have
ℓ|=r0|p|.
The angular momentum is thus equal to the distance between the line of motion of the particle and the origin times the momentum of the particle. The direction of the angular momentum vector is generally taken to be normal to the plane of the particle’s motion. For a classical particle moving under the influence of a central force, the angular momentum is conserved. The angular momentum will be used in later chapters to describe the motion of electrons about the nucleus of an atom.
The kinetic energy of a particle with mass m and velocity v is defined by the equation
E=12mv2,
where v is the magnitude of the velocity or the speed of the particle. The concept of potential energy is useful for describing the motion of particles under the influence of conservative forces. In order to define the potential energy of a particle, we choose a point of reference denoted by R. The potential energy of a particle at a point P is defined as the negative of the work carried out on the particle by the force field as the particle moves from R to P. For a one-dimensional problem described by a variable x, the definition of the potential energy can be written
P=−∫RPF(x)dx.
(I.1)
As a first example of how the potential energy is defined we consider the harmonic oscillator illustrated in Fig. I.2(a). The harmonic oscillator consists of a body of mass m moving under the influence of a linear restoring force
=−kx,
(I.2)
where x denotes the distance of the body from its equilibrium position. The constant k, which occurs in Eq. (I.2), is called the force constant. The restoring force is proportional to the displacement of the body and points in the direction opposite to the displacement. If the body is displaced to the right, for instance, the restoring force points to the left. It is natural to take the reference position R in the definition of the potential energy of the oscillator to be the equilibrium position for which x = 0. The definition of the potential energy (I.1) then becomes
(x)=−∫0x(−kx′)dx′=12kx2.
(I.3)
Here x′ is used within the integration in place of x to distinguish the variable of integration from the limit of integration.
If one were to pull the mass shown in Fig. I.2(a) from its equilibrium position and release it, the mass would oscillate with a frequency independent of the initial displacement. The angular frequency of the oscillator is related to the force constant of the oscillator and the mass of the particle by the equation
=k/m.
or
=mω2.
Substituting this expression for k into Eq. (I.3), we obtain the following expression for the potential energy of the oscillator
(x)=12mω2x2.
(I.4)
The oscillator potential is illustrated in Fig. I.2(b). The harmonic oscillator provides a useful model for a number of important problems in physics. It may be used, for instance, to describe the vibration of the atoms in a crystal about their equilibrium positions.
As a further example of potential energy, we consider the potential energy of a particle with electric charge q moving under the influence of a charge Q. According to Coulomb’s law, the electromagnetic force between the two charges is equal to
=14πϵ0Qqr2,
where r is the distance between the two charges and ϵ0 is the permittivity of free space. The reference point for the potential energy for this problem can be conveniently chosen to be at infinity where =∞ and the force is equal to zero. Using Eq. (I.1), the potential energy of the particle with charge q at a distance r from the charge Q can be written
(r)=−Qq4πϵ0∫∞r1r′2dr′.
Evaluating the above integral, one finds that the potential energy of the particle is
(r)=Qq4πϵ01r.
An application of this last formula will arise when we consider the motion of electrons in an atom. For an electron with charge −e moving in the field of an atomic nucleus having Z protons and hence a nuclear charge of Ze, the formula for the potential energy becomes
(r)=−Ze24πϵ01r.
(I.5)
The energy of a body is defined to be the sum of its kinetic and potential energies
=KE+V.
For an object moving under the influence of a conservative force, the energy is a constant of the motion.
I.1.2 Elementary Properties of Waves
We consider now some of the elementary properties of waves. Various kinds of waves arise in classical physics, and we shall encounter other examples of wave motion...
| Erscheint lt. Verlag | 24.2.2015 |
|---|---|
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Quantenphysik |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| Technik | |
| ISBN-10 | 0-12-800828-8 / 0128008288 |
| ISBN-13 | 978-0-12-800828-7 / 9780128008287 |
| Haben Sie eine Frage zum Produkt? |
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