A Modern Approach to Quantum Mechanics, 2e
by Townsend
ISBN: 9781891389788 | Copyright 2012
Instructor Requests
Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend’s text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement.. Chapters 6 through 10 cover the more traditional subjects in wave mechanics_x0014_the Schrödinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials_x0014_but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subject. Subsequent chapters are devoted to perturbation theory, identical particles, scattering, and the interaction of atoms with radiation, and an optional chapter on path integrals is also included. This new edition has been revised throughout to include many more worked examples and end-of-chapter problems, further enabling students to gain a complete mastery of quantum mechanics. It also includes new sections on quantum teleportation, the density operator, coherent states, and cavity quantum electrodynamics.AncillariesA detailed Instructors’ Manual is available for adopting professors.Art from the book may be downloaded by adopting professors.
Published under the University Science Books imprint
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Front Cover (pg. i) | |
Contents (pg. 5) | |
Preface (pg. 11) | |
CHAPTER 1 Stern–Gerlach Experiments (pg. 1) | |
1.1 The Original Stern–Gerlach Experiment (pg. 1) | |
1.2 Four Experiments (pg. 5) | |
1.3 The Quantum State Vector (pg. 10) | |
1.4 Analysis of Experiment 3 (pg. 14) | |
1.5 Experiment 5 (pg. 18) | |
1.6 Summary (pg. 21) | |
Problems (pg. 25) | |
CHAPTER 2 Rotation of Basis States and Matrix Mechanics (pg. 29) | |
2.1 The Beginnings of Matrix Mechanics (pg. 29) | |
2.2 Rotation Operators (pg. 33) | |
2.3 The Identity and Projection Operators (pg. 41) | |
2.4 Matrix Representations of Operators (pg. 46) | |
2.5 Changing Representations (pg. 52) | |
2.6 Expectation Values (pg. 58) | |
2.7 Photon Polarization and the Spin of the Photon (pg. 59) | |
2.8 Summary (pg. 65) | |
Problems (pg. 70) | |
CHAPTER 3 Angular Momentum (pg. 75) | |
3.1 Rotations Do Not Commute and Neither Do the Generators (pg. 75) | |
3.2 Commuting Operators (pg. 80) | |
3.3 The Eigenvalues and Eigenstates of Angular Momentum (pg. 82) | |
3.4 The Matrix Elements of the Raising and Lowering Operators (pg. 90) | |
3.5 Uncertainty Relations and Angular Momentum (pg. 91) | |
3.6 The Spin- 1/2 Eigenvalue Problem (pg. 94) | |
3.7 A Stern–Gerlach Experiment with Spin-1 Particles (pg. 100) | |
3.8 Summary (pg. 104) | |
Problems (pg. 106) | |
CHAPTER 4 Time Evolution (pg. 111) | |
4.1 The Hamiltonian and the Schrodinger Equation (pg. 111) | |
4.2 Time Dependence of Expectation Values (pg. 114) | |
4.3 Precession of a Spin- 1/2 Particle in a Magnetic Field (pg. 115) | |
4.4 Magnetic Resonance (pg. 124) | |
4.5 The Ammonia Molecule and the Ammonia Maser (pg. 128) | |
4.6 The Energy-Time Uncertainty Relation (pg. 134) | |
4.7 Summary (pg. 137) | |
Problems (pg. 138) | |
CHAPTER 5 A System of Two Spin-1/2 Particles (pg. 141) | |
5.1 The Basis States for a System of Two Spin-1/2 Particles (pg. 141) | |
5.2 The Hyperfine Splitting of the Ground State of Hydrogen (pg. 143) | |
5.3 The Addition of Angular Momenta for Two Spin-1/2 Particles (pg. 147) | |
5.4 The Einstein–Podolsky–Rosen Paradox (pg. 152) | |
5.5 A Nonquantum Model and the Bell Inequalities (pg. 156) | |
5.6 Entanglement and Quantum Teleportation (pg. 165) | |
5.7 The Density Operator (pg. 171) | |
5.8 Summary (pg. 181) | |
Problems (pg. 183) | |
CHAPTER 6 Wave Mechanics in One Dimension (pg. 191) | |
6.1 Position Eigenstates and the Wave Function (pg. 191) | |
6.2 The Translation Operator (pg. 195) | |
6.3 The Generator of Translations (pg. 197) | |
6.4 The Momentum Operator in the Position Basis (pg. 201) | |
6.5 Momentum Space (pg. 202) | |
6.6 A Gaussian Wave Packet (pg. 204) | |
6.7 The Double-Slit Experiment (pg. 210) | |
6.8 General Properties of Solutions to the Schrodinger Equation in Position Space (pg. 213) | |
6.9 The Particle in a Box (pg. 219) | |
6.10 Scattering in One Dimension (pg. 224) | |
6.11 Summary (pg. 234) | |
Problems (pg. 237) | |
CHAPTER 7 The One-Dimensional Harmonic Oscillator (pg. 245) | |
7.1 The Importance of the Harmonic Oscillator (pg. 245) | |
7.2 Operator Methods (pg. 247) | |
7.3 Matrix Elements of the Raising and Lowering Operators (pg. 252) | |
7.4 Position-Space Wave Functions (pg. 254) | |
7.5 The Zero-Point Energy (pg. 257) | |
7.6 The Large-n Limit (pg. 259) | |
7.7 Time Dependence (pg. 261) | |
7.8 Coherent States (pg. 262) | |
7.9 Solving the Schrodinger Equation in Position Space (pg. 269) | |
7.10 Inversion Symmetry and the Parity Operator (pg. 273) | |
7.11 Summary (pg. 274) | |
Problems (pg. 276) | |
CHAPTER 8 Path Integrals (pg. 281) | |
8.1 The Multislit, Multiscreen Experiment (pg. 281) | |
8.2 The Transition Amplitude (pg. 282) | |
8.3 Evaluating the Transition Amplitude for Short Time Intervals (pg. 284) | |
8.4 The Path Integral (pg. 286) | |
8.5 Evaluation of the Path Integral for a Free Particle (pg. 289) | |
8.6 Why Some Particles Follow the Path of Least Action (pg. 291) | |
8.7 Quantum Interference Due to Gravity (pg. 297) | |
8.8 Summary (pg. 299) | |
Problems (pg. 301) | |
CHAPTER 9 Translational and Rotational Symmetry in the Two-Body Problem (pg. 303) | |
9.1 The Elements of Wave Mechanics in Three Dimensions (pg. 303) | |
9.2 Translational Invariance and Conservation of Linear Momentum (pg. 307) | |
9.3 Relative and Center-of-Mass Coordinates (pg. 311) | |
9.4 Estimating Ground-State Energies Using the Uncertainty Principle (pg. 313) | |
9.5 Rotational Invariance and Conservation of Angular Momentum (pg. 314) | |
9.6 A Complete Set of Commuting Observables (pg. 317) | |
9.7 Vibrations and Rotations of a Diatomic Molecule (pg. 321) | |
9.8 Position-Space Representations of L in Spherical Coordinates (pg. 328) | |
9.9 Orbital Angular Momentum Eigenfunctions (pg. 331) | |
9.10 Summary (pg. 337) | |
Problems (pg. 339) | |
CHAPTER 10 Bound States of Central Potentials (pg. 345) | |
10.1 The Behavior of the Radial Wave Function Near the Origin (pg. 345) | |
10.2 The Coulomb Potential and the Hydrogen Atom (pg. 348) | |
10.3 The Finite Spherical Well and the Deuteron (pg. 360) | |
10.4 The Infinite Spherical Well (pg. 365) | |
10.5 The Three-Dimensional Isotropic Harmonic Oscillator (pg. 369) | |
10.6 Conclusion (pg. 375) | |
Problems (pg. 376) | |
CHAPTER 11 Time-Independent Perturbations (pg. 381) | |
11.1 Nondegenerate Perturbation Theory (pg. 381) | |
11.2 Degenerate Perturbation Theory (pg. 389) | |
11.3 The Stark Effect in Hydrogen (pg. 391) | |
11.4 The Ammonia Molecule in an External Electric Field Revisited (pg. 395) | |
11.5 Relativistic Perturbations to the Hydrogen Atom (pg. 398) | |
11.6 The Energy Levels of Hydrogen (pg. 408) | |
11.7 The Zeeman Effect in Hydrogen (pg. 410) | |
11.8 Summary (pg. 412) | |
Problems (pg. 413) | |
CHAPTER 12 Identical Particles (pg. 419) | |
12.1 Indistinguishable Particles in Quantum Mechanics (pg. 419) | |
12.2 The Helium Atom (pg. 424) | |
12.3 Multielectron Atoms and the Periodic Table (pg. 437) | |
12.4 Covalent Bonding (pg. 441) | |
12.5 Conclusion (pg. 448) | |
Problems (pg. 448) | |
CHAPTER 13 Scattering (pg. 451) | |
13.1 The Asymptotic Wave Function and the Differential Cross Section (pg. 451) | |
13.2 The Born Approximation (pg. 458) | |
13.3 An Example of the Born Approximation: The Yukawa Potential (pg. 463) | |
13.4 The Partial Wave Expansion (pg. 465) | |
13.5 Examples of Phase-Shift Analysis (pg. 469) | |
13.6 Summary (pg. 477) | |
Problems (pg. 478) | |
CHAPTER 14 Photons and Atoms (pg. 483) | |
14.1 The Aharonov–Bohm Effect (pg. 483) | |
14.2 The Hamiltonian for the Electromagnetic Field (pg. 488) | |
14.3 Quantizing the Radiation Field (pg. 493) | |
14.4 The Hamiltonian of the Atom and the Electromagnetic Field (pg. 501) | |
14.5 Time-Dependent Perturbation Theory (pg. 504) | |
14.6 Fermi’s Golden Rule (pg. 513) | |
14.7 Spontaneous Emission (pg. 518) | |
14.8 Cavity Quantum Electrodynamics (pg. 526) | |
14.9 Higher Order Processes and Feynman Diagrams (pg. 530) | |
Problems (pg. 533) | |
Appendix A Electromagnetic Units (pg. 539) | |
Appendix B The Addition of Angular Momenta (pg. 545) | |
Appendix C Dirac Delta Functions (pg. 549) | |
Appendix D Gaussian Integrals (pg. 553) | |
Appendix E The Lagrangian for a Charge q in a Magnetic Field (pg. 557) | |
Appendix F Values of Physical Constants (pg. 561) | |
Appendix G Answers to Selected Problems (pg. 563) | |
Index (pg. 565) | |
Back Cover (pg. 572) |
John S. Townsend
John S. Townsend is the Susan and Bruce Worster Professor of Physics at Harvey Mudd College, the science and engineering college of the Claremont Colleges. He received his B.S. from Duke University, his Ph.D. from Johns Hopkins University, and was a National Science Foundation Graduate Fellow. He has been a visiting professor at Caltech, the University of Southampton in England, Duke University and Swarthmore College, and he was a Science Fellow at the Center for International Security and Arms Control at Stanford University. He loves teaching. Townsend is also the author of Quantum Physics: A Fundamental Approach to Modern Physics.Instructors Only | |
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