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Publisher Summary 1
This classic text provides a comprehensive exposition of the concepts and techniques of quantum mechanics. The phenomena treated are sufficiently simple to allow the student to readily assess the validity of the models so that attention is not deflected from the heart of the subject. To that end, the book concentrates on systems that can either be solved exactly or be handled by well-controlled, plausible approximations. With few exceptions, this means systems with a small number of degrees of freedom. The exceptions are many 鈥?electron atoms, the electromagnetic field and the Dirac equation. The inclusion of the last two topics reflects the belief that every physicist should now have some knowledge of these cornerstones of modern physics. This new edition has been completely revised and rewritten throughout, but retains the clarity and readability of the first edition. Born in Vienna, Kurt Gottfried emigrated to Canada in 1939 and received his Ph.D. in theoretical physics from the Massachusetts Institute of Technology in 1955. He is a professor emeritus of physics at Cornell University, and had previously been at Harvard University and at CERN in Geneva, Switzerland. He is the coauthor of Concepts of Particle Physics (with V.F. Weisskopf) and of Crisis Stability and Nuclear War. Gottfried has done research in both nuclear and particle physics; he has an active interest in arms control and human rights and is a founder and currently the Chair of the Union of Concerned Scientists. Tung-Mow Yan, originally from Taiwan, received his Ph.D. in theoretical physics from Harvard University in 1968. He has been a member of the Cornell University faculty since 1970 after spending two years as a research associate at the Stanford Linear Accelerator Center. He has conducted research in many areas of elementary particle physics."A Classic Textbook Returns to the Classroom", William Harper, Physics Today
Publisher Summary 2
This text builds a solid introduction to the concepts and techniques of quantum mechanics in settings where the phenomena treated are sufficiently simple: systems that can either be solved exactly or be handled by well-controlled, plausible approximations. It includes discussions of many-electron atoms, the electromagnetic field, and the Dirac equation.
目录
Preface p. vii
Fundamental Concepts p. 1
Complementarity and Uncertainty p. 1
Complementarity p. 2
The Uncertainty Principle p. 6
Superposition p. 11
The Superposition Principle p. 11
Two-Particle States p. 12
Two-Particle Interferometry p. 14
EPR Correlations p. 19
The Discovery of Quantum Mechanics p. 20
Problems p. 24
The Formal Framework p. 27
The Formal Language: Hilbert Space p. 27
Hilbert Space p. 29
Dirac's Notation p. 30
Operators p. 32
Unitary Transformations p. 35
Eigenvalues and Eigenvectors p. 38
States and Probabilities p. 39
Quantum States p. 40
Measurement Outcomes p. 43
Mixtures and the Density Matrix p. 46
Entangled States p. 50
The Wigner Distribution p. 52
Canonical Quantization p. 54
The Canonical Commutation Rules p. 54
Schrodinger Wave Functions p. 56
Uncertainty Relations p. 59
The Equations of Motion p. 60
The Schrodinger Picture p. 60
The Heisenberg Picture p. 65
Time Development of Expectation Values p. 66
Time-Energy Uncertainty p. 67
The Interaction Picture p. 70
Symmetries and Conservation Laws p. 71
Symmetries and Unitary Transformations p. 72
Spatial Translations p. 73
Symmetry Groups p. 74
Rotations p. 76
Space Reflection and Parity p. 81
Gauge Invariance p. 82
Propagators and Green's Functions p. 84
Propagators p. 84
Green's Functions p. 85
The Free Particle Propagator and Green's Function p. 87
Perturbation Theory p. 89
The Path Integral p. 92
The Feynman Path Integral p. 92
The Free-Particle Path Integral p. 95
Semiclassical Quantum Mechanics p. 98
Hamilton-Jacobi Theory p. 99
The Semiclassical Wave Function p. 102
The Semiclassical Propagator p. 104
Derivations p. 106
Problems p. 109
Endnotes p. 111
Basic Tools p. 113
Angular Momentum: The Spectrum p. 113
Orbital Angular Momentum p. 116
Spin p. 120
Spin 1/2 p. 121
Spin 1 p. 125
Arbitrary Spins p. 127
Free-Particle States p. 128
Addition of Angular Momenta p. 133
General Results p. 133
Adding Spins 1/2 and Unit Spins p. 135
Arbitrary Angular Momenta; Clebsch-Gordan Coefficients p. 137
Matrix Elements of Vector Operators p. 140
The Two-Body Problem p. 142
Center-of-Mass and Relative Motion p. 142
The Radial Schrodinger Equation: General Case p. 144
Bound-State Coulomb Wave Functions p. 147
Basic Approximation Methods p. 149
Stationary-State Perturbation Theory p. 150
Degenerate-State Perturbation Theory p. 153
Time-Dependent Perturbation Theory p. 156
The Golden Rule p. 159
The Variational Principle p. 161
Problems p. 162
Low-Dimensional Systems p. 165
Spectroscopy in Two-Level Systems p. 166
Level Crossings p. 166
Resonance Spectroscopy p. 169
The Harmonic Oscillator p. 174
Equations of Motion p. 174
Energy Eigenvalues and Eigenfunctions p. 175
The Forced Oscillator p. 178
Coherent States p. 181
Wigner Distributions p. 184
Propagator and Path Integral p. 186
Motion in a Magnetic Field p. 188
Equations of Motion and Energy Spectrum p. 188
Eigenstates of Energy and Angular Momentum p. 190
Coherent States p. 194
The Aharonov-Bohm Effect p. 196
Scattering in One Dimension p. 198
General Properties p. 198
The Delta-Function Potential p. 202
Resonant Transmission and Reflection p. 204
The Exponential Decay Law p. 213
The Semiclassical Approximation p. 216
The WKB Approximation p. 217
Connection Formulas p. 218
Energy Eigenvalues, Barrier Transmission, and [alpha]-Decay p. 222
Exactly Solvable Examples p. 225
Problems p. 228
Endnotes p. 233
Hydrogenic Atoms p. 235
Qualitative Overview p. 235
The Keplei Problem p. 238
The Lenz Vector p. 238
The Energy Spectrum p. 240
The Conservation of M p. 242
Wave Functions p. 243
Fine and Hyperfine Structure p. 245
Fine Structure p. 245
Hyperfine Structure--General Features p. 249
Magnetic Dipole Hfs p. 250
Electric Quadrupole Hfs p. 252
The Zeeman and Stark Effects p. 254
Order of Magnitude Estimates p. 254
The n = 2 Multiplet p. 257
Strong Fields p. 260
Problems p. 263
Endnotes p. 266
Two-Electron Atoms p. 267
Two Identical Particles p. 267
Spin and Statistics p. 267
The Exclusion Principle p. 269
Symmetric and Antisymmetric States p. 270
The Spectrum of Helium p. 272
Atoms with Two Valence Electrons p. 275
The Shell Model and Coupling Schemes p. 275
The Configuration p[superscript 2] p. 276
Problems p. 279
Endnotes p. 281
Symmetries p. 283
Equivalent Descriptions and Wigner's Theorem p. 283
Time Reversal p. 286
The Time Reversal Operator p. 287
Spin 0 p. 289
Spin 1/2 p. 290
Galileo Transformations p. 292
Transformation of States: Galileo Invariance p. 292
Mass Differences p. 295
The Rotation Group p. 297
The Group SO (3) p. 297
SO (3) and SU (2) p. 299
Irreducible Representations of SU (2) p. 301
D(R) in Terms of Euler Angles p. 304
The Kronecker Product p. 306
Integration over Rotations p. 307
Some Consequences of Symmetry p. 311
Rotation of Spherical Harmonics p. 312
Helicity States p. 314
Decay Angular Distributions p. 316
Rigid-Body Motion p. 317
Tensor Operators p. 320
Definition of Tensor Operators p. 320
The Wigner-Eckart Theorem p. 322
Racah Coefficients and 6-j Symbols p. 324
Geometric Phases p. 326
Spin in Magnetic Field p. 327
Correction to the Adiabatic Approximation p. 329
Problems p. 331
Endnotes p. 334
Elastic Scattering p. 335
Consequences of Probability and Angular Momentum Conservation p. 335
Partial Waves p. 335
Hard Sphere Scattering p. 340
Time-Dependent Description and the Optical Theorem p. 340
General Properties of Elastic Amplitudes p. 345
Integral Equations and the Scattering Amplitude p. 346
A Solvable Example p. 350
Bound-State Poles p. 353
Symmetry Properties of the Amplitude p. 354
Relations Between Laboratory and Center-of-Mass Quantities p. 356
Approximations to Elastic Amplitudes p. 357
The Born Approximation p. 358
Validity of the Born Approximation p. 361
Short-Wavelength Approximations p. 364
Scattering in a Coulomb Field p. 368
The Coulomb Scattering Amplitude p. 368
The Influence of a Short-Range Interaction p. 373
Scattering of Particles with Spin p. 376
Symmetry Properties p. 377
Cross Section and Spin Polarization p. 378
Scattering of a Spin 1/2 Particle by a Spin 0 Target p. 379
Neutron-Proton Scattering and the Deuteron p. 382
Low-Energy Neutron-Proton Scattering p. 383
The Deuteron and Low-Energy np Scattering p. 385
Neutron Scattering by the Hydrogen Molecule p. 388
The Tensor Force p. 390
Scattering of Identical Particles p. 392
Boson-Boson Scattering p. 392
Fermion-Fermion Scattering p. 395
Problems p. 397
Inelastic Collisions p. 403
Atomic Collision Processes p. 403
Scattering Amplitudes and Cross Sections p. 404
Elastic Scattering p. 407
Inelastic scattering p. 409
Energy Loss p. 412
The S Matrix p. 414
Scattering by a Bound Particle p. 415
The S Matrix p. 417
Transition Rates and Cross Sections p. 421
Inelastic Resonances p. 424
A Solvable Model p. 424
Elastic and Inelastic Cross Sections p. 428
Problems p. 433
Endnotes p. 435
Electrodynamics p. 437
Quantization of the Free Field p. 437
The Classical Theory p. 438
Quantization p. 441
Photons p. 443
Space Reflection and Time Reversal p. 448
Causality and Uncertainty in Electrodynamics p. 450
Commutation Rules: Complementarity p. 450
Uncertainty Relations p. 452
Vacuum Fluctuations p. 454
The Casimir Effect p. 455
The Lamb Shift p. 458
Radiative Transitions p. 460
The Interaction Between Field and Sources p. 461
Transition Rates p. 463
Dipole Transitions p. 466
Quantum Optics p. 468
The Beam Splitter p. 468
Various States of the Field p. 470
Photon Coincidences p. 474
The Photoeffect in Hydrogen p. 476
High Energies p. 476
The Cross Section Near Threshold p. 478
Scattering of Photons p. 482
Resonant Scattering and Spontaneous Decay p. 485
Model Hamiltonian p. 486
The Elastic Scattering Cross Section p. 488
Decay of the Excited State p. 492
The Connection Between Self-Energy and Resonance Width p. 495
Problems p. 496
Endnotes p. 501
Systems of Identical Particles p. 503
Indistinguishability p. 503
Second Quantization p. 506
Bose-Einstein Statistics p. 507
Fermi-Dirac Statistics p. 513
The Equations of Motion p. 516
Distribution Functions p. 518
Ideal Gases p. 519
The Grand Canonical Ensemble p. 520
The Ideal Fermi Gas p. 521
The Ideal Bose Gas p. 524
The Mean Field Approximation p. 526
The Dilute Bose-Einstein Condensate p. 527
The Hartree-Fock Equations p. 530
Problems p. 535
Interpretation p. 539
The Critique of Einstein, Podolsky and Rosen p. 540
Hidden Variables p. 544
Bell's Theorem p. 546
The Spin Singlet State p. 547
Bell's Theorem p. 548
The Clauser-Horne Inequality p. 550
An Experimental Test of Bell's Inequality p. 551
Locality p. 554
Measurement p. 558
A Measurement Device p. 558
Coherence and Entropy Following Measurement p. 562
An Optical Analogue to the Stern-Gerlach Experiment p. 566
A Delayed Choice Experiment p. 570
Summation p. 572
Problems p. 574
Endnotes p. 575
Relativistic Quantum Mechanics p. 577
Introduction p. 577
The Dirac Equation p. 579
Lorentz Transformations of Spinors p. 580
The Free-Particle Dirac Equation p. 584
Charge and Current Densities p. 587
Electromagnetic Interaction of a Dirac Particle p. 589
The Dirac Equation in the Presence of a Field p. 589
The Magnetic Moment p. 591
The Fine Structure Hamiltonian p. 593
Antiparticles and Charge Conjugation p. 595
Scattering of Ultra-Relativistic Electrons p. 597
Bound States in a Coulomb Field p. 600
Problems p. 605
Endnotes p. 606
Appendix p. 607
Index p. 610
Fundamental Concepts p. 1
Complementarity and Uncertainty p. 1
Complementarity p. 2
The Uncertainty Principle p. 6
Superposition p. 11
The Superposition Principle p. 11
Two-Particle States p. 12
Two-Particle Interferometry p. 14
EPR Correlations p. 19
The Discovery of Quantum Mechanics p. 20
Problems p. 24
The Formal Framework p. 27
The Formal Language: Hilbert Space p. 27
Hilbert Space p. 29
Dirac's Notation p. 30
Operators p. 32
Unitary Transformations p. 35
Eigenvalues and Eigenvectors p. 38
States and Probabilities p. 39
Quantum States p. 40
Measurement Outcomes p. 43
Mixtures and the Density Matrix p. 46
Entangled States p. 50
The Wigner Distribution p. 52
Canonical Quantization p. 54
The Canonical Commutation Rules p. 54
Schrodinger Wave Functions p. 56
Uncertainty Relations p. 59
The Equations of Motion p. 60
The Schrodinger Picture p. 60
The Heisenberg Picture p. 65
Time Development of Expectation Values p. 66
Time-Energy Uncertainty p. 67
The Interaction Picture p. 70
Symmetries and Conservation Laws p. 71
Symmetries and Unitary Transformations p. 72
Spatial Translations p. 73
Symmetry Groups p. 74
Rotations p. 76
Space Reflection and Parity p. 81
Gauge Invariance p. 82
Propagators and Green's Functions p. 84
Propagators p. 84
Green's Functions p. 85
The Free Particle Propagator and Green's Function p. 87
Perturbation Theory p. 89
The Path Integral p. 92
The Feynman Path Integral p. 92
The Free-Particle Path Integral p. 95
Semiclassical Quantum Mechanics p. 98
Hamilton-Jacobi Theory p. 99
The Semiclassical Wave Function p. 102
The Semiclassical Propagator p. 104
Derivations p. 106
Problems p. 109
Endnotes p. 111
Basic Tools p. 113
Angular Momentum: The Spectrum p. 113
Orbital Angular Momentum p. 116
Spin p. 120
Spin 1/2 p. 121
Spin 1 p. 125
Arbitrary Spins p. 127
Free-Particle States p. 128
Addition of Angular Momenta p. 133
General Results p. 133
Adding Spins 1/2 and Unit Spins p. 135
Arbitrary Angular Momenta; Clebsch-Gordan Coefficients p. 137
Matrix Elements of Vector Operators p. 140
The Two-Body Problem p. 142
Center-of-Mass and Relative Motion p. 142
The Radial Schrodinger Equation: General Case p. 144
Bound-State Coulomb Wave Functions p. 147
Basic Approximation Methods p. 149
Stationary-State Perturbation Theory p. 150
Degenerate-State Perturbation Theory p. 153
Time-Dependent Perturbation Theory p. 156
The Golden Rule p. 159
The Variational Principle p. 161
Problems p. 162
Low-Dimensional Systems p. 165
Spectroscopy in Two-Level Systems p. 166
Level Crossings p. 166
Resonance Spectroscopy p. 169
The Harmonic Oscillator p. 174
Equations of Motion p. 174
Energy Eigenvalues and Eigenfunctions p. 175
The Forced Oscillator p. 178
Coherent States p. 181
Wigner Distributions p. 184
Propagator and Path Integral p. 186
Motion in a Magnetic Field p. 188
Equations of Motion and Energy Spectrum p. 188
Eigenstates of Energy and Angular Momentum p. 190
Coherent States p. 194
The Aharonov-Bohm Effect p. 196
Scattering in One Dimension p. 198
General Properties p. 198
The Delta-Function Potential p. 202
Resonant Transmission and Reflection p. 204
The Exponential Decay Law p. 213
The Semiclassical Approximation p. 216
The WKB Approximation p. 217
Connection Formulas p. 218
Energy Eigenvalues, Barrier Transmission, and [alpha]-Decay p. 222
Exactly Solvable Examples p. 225
Problems p. 228
Endnotes p. 233
Hydrogenic Atoms p. 235
Qualitative Overview p. 235
The Keplei Problem p. 238
The Lenz Vector p. 238
The Energy Spectrum p. 240
The Conservation of M p. 242
Wave Functions p. 243
Fine and Hyperfine Structure p. 245
Fine Structure p. 245
Hyperfine Structure--General Features p. 249
Magnetic Dipole Hfs p. 250
Electric Quadrupole Hfs p. 252
The Zeeman and Stark Effects p. 254
Order of Magnitude Estimates p. 254
The n = 2 Multiplet p. 257
Strong Fields p. 260
Problems p. 263
Endnotes p. 266
Two-Electron Atoms p. 267
Two Identical Particles p. 267
Spin and Statistics p. 267
The Exclusion Principle p. 269
Symmetric and Antisymmetric States p. 270
The Spectrum of Helium p. 272
Atoms with Two Valence Electrons p. 275
The Shell Model and Coupling Schemes p. 275
The Configuration p[superscript 2] p. 276
Problems p. 279
Endnotes p. 281
Symmetries p. 283
Equivalent Descriptions and Wigner's Theorem p. 283
Time Reversal p. 286
The Time Reversal Operator p. 287
Spin 0 p. 289
Spin 1/2 p. 290
Galileo Transformations p. 292
Transformation of States: Galileo Invariance p. 292
Mass Differences p. 295
The Rotation Group p. 297
The Group SO (3) p. 297
SO (3) and SU (2) p. 299
Irreducible Representations of SU (2) p. 301
D(R) in Terms of Euler Angles p. 304
The Kronecker Product p. 306
Integration over Rotations p. 307
Some Consequences of Symmetry p. 311
Rotation of Spherical Harmonics p. 312
Helicity States p. 314
Decay Angular Distributions p. 316
Rigid-Body Motion p. 317
Tensor Operators p. 320
Definition of Tensor Operators p. 320
The Wigner-Eckart Theorem p. 322
Racah Coefficients and 6-j Symbols p. 324
Geometric Phases p. 326
Spin in Magnetic Field p. 327
Correction to the Adiabatic Approximation p. 329
Problems p. 331
Endnotes p. 334
Elastic Scattering p. 335
Consequences of Probability and Angular Momentum Conservation p. 335
Partial Waves p. 335
Hard Sphere Scattering p. 340
Time-Dependent Description and the Optical Theorem p. 340
General Properties of Elastic Amplitudes p. 345
Integral Equations and the Scattering Amplitude p. 346
A Solvable Example p. 350
Bound-State Poles p. 353
Symmetry Properties of the Amplitude p. 354
Relations Between Laboratory and Center-of-Mass Quantities p. 356
Approximations to Elastic Amplitudes p. 357
The Born Approximation p. 358
Validity of the Born Approximation p. 361
Short-Wavelength Approximations p. 364
Scattering in a Coulomb Field p. 368
The Coulomb Scattering Amplitude p. 368
The Influence of a Short-Range Interaction p. 373
Scattering of Particles with Spin p. 376
Symmetry Properties p. 377
Cross Section and Spin Polarization p. 378
Scattering of a Spin 1/2 Particle by a Spin 0 Target p. 379
Neutron-Proton Scattering and the Deuteron p. 382
Low-Energy Neutron-Proton Scattering p. 383
The Deuteron and Low-Energy np Scattering p. 385
Neutron Scattering by the Hydrogen Molecule p. 388
The Tensor Force p. 390
Scattering of Identical Particles p. 392
Boson-Boson Scattering p. 392
Fermion-Fermion Scattering p. 395
Problems p. 397
Inelastic Collisions p. 403
Atomic Collision Processes p. 403
Scattering Amplitudes and Cross Sections p. 404
Elastic Scattering p. 407
Inelastic scattering p. 409
Energy Loss p. 412
The S Matrix p. 414
Scattering by a Bound Particle p. 415
The S Matrix p. 417
Transition Rates and Cross Sections p. 421
Inelastic Resonances p. 424
A Solvable Model p. 424
Elastic and Inelastic Cross Sections p. 428
Problems p. 433
Endnotes p. 435
Electrodynamics p. 437
Quantization of the Free Field p. 437
The Classical Theory p. 438
Quantization p. 441
Photons p. 443
Space Reflection and Time Reversal p. 448
Causality and Uncertainty in Electrodynamics p. 450
Commutation Rules: Complementarity p. 450
Uncertainty Relations p. 452
Vacuum Fluctuations p. 454
The Casimir Effect p. 455
The Lamb Shift p. 458
Radiative Transitions p. 460
The Interaction Between Field and Sources p. 461
Transition Rates p. 463
Dipole Transitions p. 466
Quantum Optics p. 468
The Beam Splitter p. 468
Various States of the Field p. 470
Photon Coincidences p. 474
The Photoeffect in Hydrogen p. 476
High Energies p. 476
The Cross Section Near Threshold p. 478
Scattering of Photons p. 482
Resonant Scattering and Spontaneous Decay p. 485
Model Hamiltonian p. 486
The Elastic Scattering Cross Section p. 488
Decay of the Excited State p. 492
The Connection Between Self-Energy and Resonance Width p. 495
Problems p. 496
Endnotes p. 501
Systems of Identical Particles p. 503
Indistinguishability p. 503
Second Quantization p. 506
Bose-Einstein Statistics p. 507
Fermi-Dirac Statistics p. 513
The Equations of Motion p. 516
Distribution Functions p. 518
Ideal Gases p. 519
The Grand Canonical Ensemble p. 520
The Ideal Fermi Gas p. 521
The Ideal Bose Gas p. 524
The Mean Field Approximation p. 526
The Dilute Bose-Einstein Condensate p. 527
The Hartree-Fock Equations p. 530
Problems p. 535
Interpretation p. 539
The Critique of Einstein, Podolsky and Rosen p. 540
Hidden Variables p. 544
Bell's Theorem p. 546
The Spin Singlet State p. 547
Bell's Theorem p. 548
The Clauser-Horne Inequality p. 550
An Experimental Test of Bell's Inequality p. 551
Locality p. 554
Measurement p. 558
A Measurement Device p. 558
Coherence and Entropy Following Measurement p. 562
An Optical Analogue to the Stern-Gerlach Experiment p. 566
A Delayed Choice Experiment p. 570
Summation p. 572
Problems p. 574
Endnotes p. 575
Relativistic Quantum Mechanics p. 577
Introduction p. 577
The Dirac Equation p. 579
Lorentz Transformations of Spinors p. 580
The Free-Particle Dirac Equation p. 584
Charge and Current Densities p. 587
Electromagnetic Interaction of a Dirac Particle p. 589
The Dirac Equation in the Presence of a Field p. 589
The Magnetic Moment p. 591
The Fine Structure Hamiltonian p. 593
Antiparticles and Charge Conjugation p. 595
Scattering of Ultra-Relativistic Electrons p. 597
Bound States in a Coulomb Field p. 600
Problems p. 605
Endnotes p. 606
Appendix p. 607
Index p. 610
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