The Physics Handbook Fundamentals and Key Equations

by Poole, Charles P.

• ISBN13: 9783527406999
• ISBN10: 3527406999
• Edition: 2nd
• Format: Paperback
• Copyright: 2007-02-27
• Publisher: Wiley-VCH

Summary

This compendium of physics covers the key equations and fundamental principles that are taught in graduate programs. It offers a succinct yet systematic treatment of all areas of physics, including mathematical physics, solid state physics, particle physics, statistical mechanics, and optics. In one complete, self-contained volume, author Charles P. Poole provides both review material for students preparing for PhD qualifying examinations and a quick reference for physicists who need to brush up on basic topics or delve into areas outside their expertise. In this second edition the author devotes two chapters to such regularly needed information as trigonometric and vector identities and special functions. The remaining chapters incorporate less frequently summoned concepts, including Lagrangians, parity, dispersion relations, chaos, free energies, statistical mechanical ensembles, and elementary particle classification. A brand new chapter on entanglement and quantum computing has been added, making this an indispensable resource for graduate students and physicists in both industry and academia.

Author Biography

Charles P. Poole, Jr., Ph.D., is professor emeritus in the Department of Physics and Astronomy at the University of South Carolina. He is the author or coauthor of a dozen books, including Superconductivity and Introduction to Renormalization Group Methods. He has taught qualifying examination preparation courses for more than two decades.

Table of Contents

Preface	p. xvii
Physical Constants	p. xix
Lagrangian and Hamiltonian Formulations	p. 1
Introduction	p. 1
Newton's Law Approach	p. 2
Lagrangian Formulation	p. 3
Hamiltonian Formulation	p. 6
Variational Principles and Virtual Displacements	p. 8
Central Forces	p. 10
Introduction	p. 10
Action and Reaction	p. 11
Two-Particle Central Force Motion	p. 12
Equations and Orbits of the Motion	p. 15
Bound and Closed Orbits	p. 19
Open Orbits and Scattering	p. 22
Three-Body Problem	p. 24
Rigid Bodies	p. 28
Introduction	p. 28
Nature and Orientation of a Rigid Body	p. 29
Rotation Matrices	p. 32
Vector and Tensor Transformations	p. 33
Parity	p. 34
Two-Dimensional Representation of Rotations	p. 35
Rotating Coordinate Systems and Coriolis Force	p. 36
Rotating Bodies	p. 38
Oscillations and Variations	p. 42
Introduction	p. 42
Molecular Vibrations	p. 43
Rigid Body	p. 43
Normal Modes	p. 45
Triatomic Molecule	p. 46
Linear Chain of N Atoms	p. 48
Dispersion Relations	p. 51
Diatomic Linear Chain	p. 52
Vibrating Solids	p. 54
Molecular Rotations	p. 55
Molecular Vibrational Spectroscopy	p. 57
Canonical Transformations	p. 59
Introduction	p. 59
Nature of the Canonical Transformation	p. 60
Harmonic Oscillator	p. 61
Hamilton-Jacobi Equation	p. 62
Action-Angle Variables	p. 64
Poisson Brackets	p. 66
Non-Linear Dynamics and Chaos	p. 68
Introduction	p. 68
Perturbation Theory	p. 69
Harmonic Oscillator in Phase Space	p. 70
System Trajectories on N-Tori	p. 71
Stability of Perturbed Orbits and Chaos	p. 72
Logistic Equation or Quadratic Iterator	p. 73
Characteristics and Constants of Chaos	p. 78
Chaos in Different Systems	p. 81
Relativity	p. 87
Introduction	p. 87
Newtonian Mechanics	p. 88
Constancy of Speed of Light	p. 88
Lorentz Transformation	p. 89
Past and Future	p. 91
Lorentz Contraction and Time Dilatation	p. 94
Doppler Shift	p. 95
Newton's Law	p. 96
Scalar Products and Invariants	p. 97
More General Transformations	p. 98
Thermodynamics	p. 101
Introduction	p. 102
Exact and Inexact Differentials	p. 102
Laws of Thermodynamics	p. 103
Heat Engine and Carnot Cycle	p. 105
Internal Energy, Enthalpy, and Free Energies	p. 107
Maxwell Relations	p. 108
Gibbs Phase Rule	p. 109
Changes of Phase	p. 110
Specific Heat of Ideal Gas	p. 112
Adiabatic Gas Law	p. 113
Specific Heat of Solids	p. 114
Thermoelectric and Thermomagnetic Effects	p. 116
Negative Temperatures	p. 121
Statistical Mechanics	p. 121
Statistical Mechanics and Distribution Functions	p. 123
Introduction	p. 123
Microcanonical Ensemble	p. 125
Canonical Ensemble	p. 125
Grand Canonical Ensemble	p. 127
Thermodynamics	p. 129
Paramagnetism	p. 130
Entropy and Adiabatic Demagnetization	p. 132
Maxwell Distribution	p. 133
Classical and Quantum Statistics	p. 134
Distribution Functions	p. 137
Photon Statistics	p. 138
Ortho-Para Statistics	p. 140
Electrostatics and Magnetostatics	p. 142
Introduction	p. 143
Electric and Magnetic Fields	p. 143
Maxwell's Equations	p. 144
Electromagnetic Potentials	p. 145
Dielectric Constant and Permeability	p. 146
Boundary Conditions at Interfaces between Media	p. 00147
Sources of Electric Field	p. 148
Sources of Magnetic Field	p. 150
Electrostatics	p. 152
Boundary Conditions at Surfaces	p. 153
Solving Potential Problems	p. 154
Tesseral and Spherical Harmonics	p. 155
Magnetostatics	p. 156
Faraday's Law	p. 159
Multipoles and Media	p. 160
Introduction	p. 160
Electric Multipoles	p. 161
Electric Dipole Fields	p. 164
Energy and Torque	p. 164
Magnetic Multipoles	p. 166
Magnetic Moments	p. 167
Dielectric Constant and Permeability	p. 168
Ellipsoids in Electric and Magnetic Fields	p. 170
Nuclear and Atomic Multipoles	p. 174
Relativistic Electrodynamics	p. 176
Introduction	p. 176
Electromagnetic Field Tensor	p. 177
Invariants	p. 179
Field Tensor and Potentials	p. 180
Gauge Transformations	p. 182
Motion of Charge in Electromagnetic Fields	p. 183
Perpendicular Fields	p. 184
Adiabatic Invariants	p. 186
Wave Propagation	p. 188
Introduction	p. 188
Plane Waves	p. 189
Reflection and Refraction	p. 191
Reflection, Refraction, and Transmission at Oblique Incidence	p. 193
Polarization	p. 195
Absorption and Dispersion	p. 196
Conducting Media	p. 197
Guided Waves	p. 200
Modulated Waves	p. 201
Solitons	p. 202
Optics	p. 206
Introduction	p. 206
Index of Refraction	p. 207
Lenses	p. 207
Mirrors	p. 209
Polarization	p. 210
Interference and Diffraction	p. 212
Interference	p. 213
Single, Double, and Multiple Slits	p. 215
Radiation	p. 219
Introduction	p. 219
Radiating Charge and Current Distributions	p. 220
Radiation Zones	p. 221
Electric Dipole Radiation	p. 222
Charge in Uniform Motion	p. 224
Accelerated Charge	p. 226
Slowly Moving Accelerated Charge	p. 226
Relativistically Accelerated Charge	p. 227
Cherenkov Radiation	p. 230
Transition Radiation	p. 231
Collisions	p. 233
Introduction	p. 233
Coulomb Collision	p. 234
Collisions with Nuclei	p. 237
Bremsstrahlung	p. 239
Thomson Scattering	p. 240
Angular Momentum	p. 242
Introduction	p. 242
Linear and Angular Momentum	p. 243
Momentum Operators	p. 244
Orbital and Spin Angular Momentum	p. 246
Spin-Orbit Interaction	p. 248
Wave Functions and Clebsch Gordan Coefficients	p. 249
Irreducible Tensors	p. 251
Matrix Formulation of Quantum Mechanics	p. 255
Introduction	p. 255
Angular Momentum Matrices	p. 256
Addition of Angular Momentum	p. 258
Zeeman Effect of Hydrogen Atom	p. 259
General Hamiltonian Matrix	p. 262
Schrodinger Equation	p. 264
Introduction	p. 264
The Hamiltonian	p. 265
Laplacian Operator and Radial Equation	p. 266
Three-Dimensional Square Well	p. 267
Infinite Square Well	p. 269
Three-Dimensional Harmonic Oscillator	p. 270
One-Dimensional Quantum Systems	p. 275
Introduction	p. 275
Schrodinger Equation	p. 276
Reflection at the Potential Step	p. 278
Transmission Past the Potential Step	p. 279
Potential Barrier	p. 281
Square Well Potential	p. 283
Infinite Square Well	p. 288
Atoms	p. 290
Introduction	p. 290
The Hydrogen Atom	p. 291
Spin-Orbit Interaction	p. 295
The Helium Atom	p. 296
Energies and Sizes of Atoms	p. 299
Hartree-Fock Method	p. 304
Perturbation Theory	p. 306
Introduction	p. 306
Power Series Expansion	p. 307
Time Independent Perturbations	p. 308
Hydrogen Atom Zeeman Effect	p. 309
Degenerate Perturbation Theory	p. 312
Time Dependent Perturbations	p. 313
Transition Probability	p. 316
Scattering	p. 317
Fluids and Solids	p. 319
Introduction	p. 319
Gases	p. 320
Phase Transitions	p. 322
Liquid State and Fluctuations	p. 323
Diffusion	p. 326
Structure of Solids	p. 327
Close Packing	p. 328
Direct and Reciprocal Lattice	p. 331
Crystal Structure Determination	p. 332
Wigner-Seitz Cell	p. 334
Phonons and Other Particles	p. 336
Superconductivity	p. 338
Conduction in Solids	p. 340
Introduction	p. 340
Electron Transport Theories	p. 342
Electrical Conductivity	p. 343
AC Electrical Conductivity	p. 344
Resistivity	p. 345
Thermal Conductivity	p. 346
Fermi Surface	p. 347
Energy Bands in Two Dimensions	p. 354
Semiconductors	p. 357
Hall Effect	p. 360
Nuclei	p. 363
Introduction	p. 363
Fundamental Forces	p. 364
Size of the Nucleus	p. 366
Binding Energy	p. 367
Shell Model	p. 369
Radioactive Decay	p. 371
Helicity and Parity Non-Conservation	p. 375
Mossbauer Effect	p. 376
Carbon Dating and the Carbon Cycle	p. 377
Elementary Particles	p. 379
Introduction	p. 379
Characteristics of the Fundamental Forces	p. 380
Particle Characteristics	p. 383
Three-Quark Model	p. 385
Conservation Laws and Reactions	p. 393
Leptons	p. 395
Color, Charm, Beauty, and Truth	p. 395
Mathematical Physics: Tensors and Matrices	p. 399
Introduction	p. 400
Vector Relations	p. 400
Coordinate Systems	p. 402
Determinants	p. 407
Matrices	p. 408
Pauli Matrices and Spinors	p. 412
Tensors	p. 413
Infinite Series	p. 415
Fourier Series	p. 416
Fourier Transforms	p. 418
Integral Transforms and Equations	p. 421
Complex Variables	p. 425
Contour Integration	p. 427
Group Theory	p. 430
Monte Carlo Method	p. 436
Mathematical Physics: Differential Equations and Orthogonal Functions	p. 437
Introduction	p. 347
First-Order Differential Equations	p. 438
Second-Order Differential Equations	p. 439
Laplace and Helmholtz Equations	p. 447
Bessel Functions	p. 450
Legendre Polynomials	p. 457
Spherical Harmonics	p. 459
Gamma and Related Functions	p. 462
Delta Functions	p. 467
Green's Functions	p. 469
Entanglement and Quantum Computing	p. 471
Introduction	p. 471
Unitary Transformations of Qubits	p. 472
Entangled States	p. 476
Testing for Entanglement	p. 479
Factoring Large Numbers Classically	p. 482
Factoring Large Numbers with a Quantum Computer	p. 485
Implementing Quantum Computers	p. 489
Bibliography	p. 491
Index	p. 495
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