Relativity 1
1.1 Special Relativity 2
All motion is relative; the speed of light in free space is the same
for all observers
1.2 Time Dilation 5
A moving clock ticks more slowly than a clock at rest
1.3 Doppler Effect 10
Why the universe is believed to be expanding
1.4 Length Contraction 15
Faster means shorter
1.5 Twin Paradox 17
A longer life, but it will not seem longer
1.6 Electricity and Magnetism 19
Relativity is the bridge
1.7 Relativistic Momentum 22
Redefining an important quantity
1.8 Mass and Energy 26
Where E0 mc2 comes from
1.9 Energy and Momentum 30
How they fit together in relativity
1.10 General Relativity 33
Gravity is a warping of spacetime
APPENDIX I: The Lorentz Transformation 37
APPENDIX II: Spacetime 46
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CHAPTER 2
Particle Properties of Waves 52
2.1 Electromagnetic Waves 53
Coupled electric and magnetic oscillations that move with the speed of
light and exhibit typical wave behavior
2.2 Blackbody Radiation 57
Only the quantum theory of light can explain its origin
2.3 Photoelectric Effect 62
The energies of electrons liberated by light depend on the frequency
of the light
2.4 What Is Light? 67
Both wave and particle
2.5 X-Rays 68
They consist of high-energy photons
2.6 X-Ray Diffraction 72
How x-ray wavelengths can be determined
2.7 Compton Effect 75
Further confirmation of the photon model
2.8 Pair Production 79
Energy into matter
2.9 Photons and Gravity 85
Although they lack rest mass, photons behave as though they have
gravitational mass
CHAPTER 3
Wave Properties of Particles 92
3.1 De Broglie Waves 93
A moving body behaves in certain ways as though it has a wave nature
3.2 Waves of What? 95
Waves of probability
3.3 Describing a Wave 96
A general formula for waves
3.4 Phase and Group Velocities 99
A group of waves need not have the same velocity as the waves
themselves
3.5 Particle Diffraction 104
An experiment that confirms the existence of de Broglie waves
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3.6 Particle in a Box 106
Why the energy of a trapped particle is quantized
3.7 Uncertainty Principle I 108
We cannot know the future because we cannot know the present
3.8 Uncertainty Principle II 113
A particle approach gives the same result
3.9 Applying the Uncertainty Principle 114
A useful tool, not just a negative statement
CHAPTER 4
Atomic Structure 119
4.1 The Nuclear Atom 120
An atom is largely empty space
4.2 Electron Orbits 124
The planetary model of the atom and why it fails
4.3 Atomic Spectra 127
Each element has a characteristic line spectrum
4.4 The Bohr Atom 130
Electron waves in the atom
4.5 Energy Levels and Spectra 133
A photon is emitted when an electron jumps from one energy level to a
lower level
4.6 Correspondence Principle 138
The greater the quantum number, the closer quantum physics approaches
classical physics
4.7 Nuclear Motion 140
The nuclear mass affects the wavelengths of spectral lines
4.8 Atomic Excitation 142
How atoms absorb and emit energy
4.9 The Laser 145
How to produce light waves all in step
APPENDIX: Rutherford Scattering 152
CHAPTER 5
Quantum Mechanics 160
5.1 Quantum Mechanics 161
Classical mechanics is an approximation of quantum mechanics
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5.2 The Wave Equation 163
It can have a variety of solutions, including complex ones
5.3 Schrödinger’s Equation: Time-Dependent Form 166
A basic physical principle that cannot be derived from anything else
5.4 Linearity and Superposition 169
Wave functions add, not probabilities
5.5 Expectation Values 170
How to extract information from a wave function
5.6 Operators 172
Another way to find expectation values
5.7 Schrödinger’s Equation: Steady-State Form 174
Eigenvalues and eigenfunctions
5.8 Particle in a Box 177
How boundary conditions and normalization determine wave functions
5.9 Finite Potential Well 183
The wave function penetrates the walls, which lowers the energy levels
5.10 Tunnel Effect 184
A particle without the energy to pass over a potential barrier may still
tunnel through it
5.11 Harmonic Oscillator 187
Its energy levels are evenly spaced
APPENDIX: The Tunnel Effect 193
CHAPTER 6
Quantum Theory of the Hydrogen Atom 200
6.1 Schrödinger’s Equation for the Hydrogen Atom
6.2 Separation of Variables 203
A differential equation for each variable
6.3 Quantum Numbers 205
Three dimensions, three quantum numbers
6.4 Principal Quantum Number 207
Quantization of energy
6.5 Orbital Quantum Number 208
Quantization of angular-momentum magnitude
6.6 Magnetic Quantum Number 210
Quantization of angular-momentum direction
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6.7 Electron Probability Density 212
No definite orbits
6.8 Radiative Transitions 218
What happens when an electron goes from one state to another
6.9 Selection Rules 220
Some transitions are more likely to occur than others
6.10 Zeeman Effect 223
How atoms interact with a magnetic field
CHAPTER 7
Many-Electron Atoms 228
7.1 Electron Spin 229
Round and round it goes forever
7.2 Exclusion Principle 231
A different set of quantum numbers for each electron in an atom
7.3 Symmetric and Antisymmetric Wave Functions 233
Fermions and bosons
7.4 Periodic Table 235
Organizing the elements
7.5 Atomic Structures 238
Shells and subshells of electrons
7.6 Explaining the Periodic Table 240
How an atom’s electron structure determines its chemical behavior
7.7 Spin-Orbit Coupling 247
Angular momenta linked magnetically
7.8 Total Angular Momentum 249
Both magnitude and direction are quantized
7.9 X-Ray Spectra 254
They arise from transitions to inner shells
APPENDIX: Atomic Spectra 259
CHAPTER 8
Molecules 266
8.1 The Molecular Bond 267
Electric forces hold atoms together to form molecules
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8.2 Electron Sharing 269
The mechanism of the covalent bond
8.3 The H2
Molecular Ion 270
Bonding requires a symmetric wave function
8.4 The Hydrogen Molecule 274
The spins of the electrons must be antiparallel
8.5 Complex Molecules 276
Their geometry depends on the wave functions of the outer electrons of
their atoms
8.6 Rotational Energy Levels 282
Molecular rotational spectra are in the microwave region
8.7 Vibrational Energy Levels 285
A molecule may have many different modes of vibration
8.8 Electronic Spectra of Molecules 291
How fluorescence and phsophorescence occur
CHAPTER 9
Statistical Mechanics 296
9.1 Statistical Distributions 297
Three different kinds
9.2 Maxwell-Boltzmann Statistics 298
Classical particles such as gas molecules obey them
9.3 Molecular Energies in an Ideal Gas 300
They vary about an average of
3
2
kT
9.4 Quantum Statistics 305
Bosons and fermions have different distribution functions
9.5 Rayleigh-Jeans Formula 311
The classical approach to blackbody radiation
9.6 Planck Radiation Law 313
How a photon gas behaves
9.7 Einstein’s Approach 318
Introducing stimulated emission
9.8 Specific Heats of Solids 320
Classical physics fails again
9.9 Free Electrons in a Metal 323
No more than one electron per quantum stat
9.10 Electron-Energy Distribution 325
Why the electrons in a metal do not contribute to its specific heat except
at very high and very low temperatures
9.11 Dying Stars 327
What happens when a star runs out of fuel
CHAPTER 10
The Solid State 335
10.1 Crystalline and Amorphous Solids 336
Long-range and short-range order
10.2 Ionic Crystals 338
The attraction of opposites can produce a stable union
10.3 Covalent Crystals 342
Shared electrons lead to the strongest bonds
10.4 Van der Waals Bond 345
Weak but everywhere
10.5 Metallic Bond 348
A gas of free electrons is responsible for the characteristic properties
of a metal
10.6 Band Theory of Solids 354
The energy band structure of a solid determines whether it is a conductor,
an insulator, or a semiconductor
10.7 Semiconductor Devices 361
The properties of the p-n junction are responsible for the microelectronics
industry
10.8 Energy Bands: Alternative Analysis 369
How the periodicity of a crystal lattice leads to allowed and forbidden bands
10.9 Superconductivity 376
No resistance at all, but only at very low temperatures (so far)
10.10 Bound Electron Pairs 381
The key to superconductivity
CHAPTER 11
Nuclear Structure 387
11.1 Nuclear Composition 388
Atomic nuclei of the same element have the same numbers of protons
but can have different numbers of neutrons
11.2 Some Nuclear Properties 392
Small in size, a nucleus may have angular momentum and a magnetic
moment
11.3 Stable Nuclei 396
Why some combinations of neutrons and protons are more stable
than others
11.4 Binding Energy 399
The missing energy that keeps a nucleus together
11.5 Liquid-Drop Model 403
A simple explanation for the binding-energy curve
11.6 Shell Model 408
Magic numbers in the nucleus
11.7 Meson Theory of Nuclear Forces 412
Particle exchange can produce either attraction or repulsion
CHAPTER 12
Nuclear Transformations 418
12.1 Radioactive Decay 419
Five kinds
12.2 Half-Life 424
Less and less, but always some left
12.3 Radioactive Series 430
Four decay sequences that each end in a stable daughter
12.4 Alpha Decay 432
Impossible in classical physics, it nevertheless occurs
12.5 Beta Decay 436
Why the neutrino should exist and how it was discovered
12.6 Gamma Decay 440
Like an excited atom, an excited nucleus can emit a photon
12.7 Cross Section 441
A measure of the likelihood of a particular interaction
12.8 Nuclear Reactions 446
In many cases, a compound nucleus is formed first
12.9 Nuclear Fission 450
Divide and conquer
12.10 Nuclear Reactors 454
E0 mc2 $$$
12.11 Nuclear Fusion in Stars 460
How the sun and stars get their energy
12.12 Fusion Reactors 463
The energy source of the future?
APPENDIX: Theory of Alpha Decay 468
CHAPTER 13
Elementary Particles 474
13.1 Interactions and Particles 475
Which affects which
13.2 Leptons 477
Three pairs of truly elementary particles
13.3 Hadrons 481
Particles subject to the strong interaction
13.4 Elementary Particle Quantum Numbers 485
Finding order in apparent chaos
13.5 Quarks 489
The ultimate constituents of hadrons
13.6 Field Bosons 494
Carriers of the interactions
13.7 The Standard Model and Beyond 496
Putting it all together
13.8 History of the Universe 498
It began with a bang
13.9 The Future 501
“In my beginning is my end.” (T. S. Eliot, Four Quartets)
APPENDIX