
Quantum Mechanics
Fundamentals
By:Â Kurt Gottfried, Tung-Mow Yan
Hardcover | 19 June 2003 | Edition Number 2
At a Glance
644 Pages
Revised
24.77 x 15.24 x 3.18
Hardcover
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Industry Reviews
JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL (27 FEBRUARY 2004)
"... [The first edition] has become one of the most used and respected accounts of quantum theory ... Gottfried and Yan's book contains a vast amount of knowledge and understanding. As well as explaining the way in which quantum theory works, it attempts to illuminate fundamental aspects of the theory ... For use with a well-constructed course (and, of course, this is the avowed purpose of the book; a useful range of problems is provided for each chapter), or for the relative expert getting to grips with particular aspects of the subject or aiming for a deeper understanding, the book is certainly ideal."
PHYSICS TODAY (August 2004)
"...especially useful for graduate students and professors who have time to go beyond the bare essentials of a topic and explore it in depth... I would recommend the book for its lucid discussions of less familiar topics alone, but the authors do not short-change the standardsubjects... I expect the second edition of Gottfried and Yan to join my library of well thumbed-through texts."
From the reviews of the second edition:
"The book under review offers the reader in-depth physical and mathematical understanding of quantum mechanics. The book is the second edition of Gottfried's Quantum mechanics. ... Readers' anticipations have finally been rewarded by the second edition of the earlier book, which is a complete revision covering most of the topics and much more ... . The appendix contains the values of important physical constants, some useful operator identities ... . The end notes at the conclusion of each chapter contain many useful references." (Howard E. Brandt, Mathematical Reviews, Issue 2007 f)
| 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 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
ISBN: 9780387955766
ISBN-10: 0387955763
Series: Graduate Texts in Contemporary Physics
Published: 19th June 2003
Format: Hardcover
Language: English
Number of Pages: 644
Audience: College, Tertiary and University
Publisher: Springer Nature B.V.
Country of Publication: US
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 24.77 x 15.24 x 3.18
Weight (kg): 1.02
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