A Modern Approach to Quantum Mechanics 2nd Edition by John S. Townsend, ISBN-13: 978-1891389788


A Modern Approach to Quantum Mechanics 2nd Edition by John S. Townsend, ISBN-13: 978-1891389788

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  • Publisher: ‎ University Science Books; 2nd edition (February 24, 2012)
  • Language: ‎ English
  • 571 pages
  • ISBN-10: ‎ 1891389785
  • ISBN-13: ‎ 978-1891389788

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-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-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.

Table of Contents:

Preface xi
Stern-Gerlach Experiments 1
The Original Stern-Gerlach Experiment 1
Four Experiments 5
The Quantum State Vector 10
Analysis of Experiment 3 14
Experiment5 18
Summary 21
Problems 25
Rotation of Basis States and Matrix Mechanics 29
The Beginnings of Matrix Mechanics 29 Rotation Operators 33 The Identity and Projection Operators 41 Matrix Representations of Operators 46 Changing Representations 52 Expectation Values 58
Photon Polarization and the Spin of the Photon 59 Summary 65
Problems 70
Angular Momentum 75
Rotations Do Not Commute and Neither Do the Generators 75 Commuting Operators 80
The Eigenvalues and Eigenstates of Angular Momentum 82
The Matrix Elements of the Raising and Lowering Operators 90
Uncertainty Relations and Angular Momentum 91
The Spin-^ Eigenvalue Problem 94
A Stern-Gerlach Experiment with Spin-1 Particles 100
Summary 104
Problems 106
Time Evolution 111
The Hamiltonian and the Schrodinger Equation 111 Time Dependence of Expectation Values 114 Precession of a Spin-| Particle in a Magnetic Field 115 Magnetic Resonance 124
The Ammonia Molecule and the Ammonia Maser 128 The Energy-Time Uncertainty Relation 134 Summary 137 Problems 138
A System of Two Spin-1/2 Particles 141
The Basis States for a System of Two Spin-| Particles 141 The Hyperfine Splitting of the Ground State of Hydrogen 143 The Addition of Angular Momenta for Two Spin- ^ Particles 147 The Einstein-Podolsky-Rosen Paradox 152 A Nonquantum Model and the Bell Inequalities 156 Entanglement and Quantum Teleportation 165 The Density Operator 171 Summary 181 Problems 183
Wave Mechanics in One Dimension 191
Position Eigenstates and the Wave Function 191
The Translation Operator 195
The Generator of Translations 197
The Momentum Operator in the Position Basis 201
Momentum Space 202
A Gaussian Wave Packet 204
The Double-Slit Experiment 210
General Properties of Solutions to the Schrodinger Equation in Position Space 213
The Particle in a Box 219 Scattering in One Dimension 224 Summary 234 Problems 237
The One-Dimensional Harmonic Oscillator 245
7.1 The Importance of the Harmonic Oscillator 245
7.2 Operator Methods 247
7.3 Matrix Elements of the Raising and Lowering Operators 252
7.4 Position-Space Wave Functions 254
7.5 The Zero-Point Energy 257
7.6 The Large-n Limit 259
7.7 Time Dependence 261
7.8 Coherent States 262
7.9 Solving the Schrodinger Equation in Position Space 269
7.10 Inversion Symmetry and the Parity Operator 273
7.11 Summary 274 Problems 276
chapter 8 Path Integrals 281
8.1 The Multislit, Multiscreen Experiment 281
8.2 The Transition Amplitude 282
8.3 Evaluating the Transition Amplitude for Short Time Intervals 284
8.4 The Path Integral 286
8.5 Evaluation of the Path Integral for a Free Particle 289
8.6 Why Some Particles Follow the Path of Least Action 291
8.7 Quantum Interference Due to Gravity 297
8.8 Summary 299 Problems 301
chapter 9 Translational and Rotational Symmetry in the Two-Body Problem 303
9.1 The Elements of Wave Mechanics in Three Dimensions 303
9.2 Translational Invariance and Conservation of Linear Momentum 307
9.3 Relative and Center-of-Mass Coordinates 311
9.4 Estimating Ground-State Energies Using the Uncertainty Principle 313
9.5 Rotational Invariance and Conservation of Angular Momentum 314
9.6 A Complete Set of Commuting Observables 317
9.7 Vibrations and Rotations of a Diatomic Molecule 321
9.8 Position-Space Representations of L in Spherical Coordinates 328
9.9 Orbital Angular Momentum Eigenfunctions 331
9.10 Summary 337
Problems 339
Bound States of Central Potentials 345
The Behavior of the Radial Wave Function Near the Origin 345 The Coulomb Potential and the Hydrogen Atom 348 The Finite Spherical Well and the Deuteron 360 The Infinite Spherical Well 365
The Three-Dimensional Isotropic Harmonic Oscillator 369 Conclusion 375 Problems 376
Time-Independent Perturbations 381
Nondegenerate Perturbation Theory 381
Degenerate Perturbation Theory 389
The Stark Effect in Hydrogen 391
The Ammonia Molecule in an External Electric Field
Revisited 395
Relativistic Perturbations to the Hydrogen Atom 398 The Energy Levels of Hydrogen 408 The Zeeman Effect in Hydrogen 410 Summary 412 Problems 413
Identical Particles 419
Indistinguishable Particles in Quantum Mechanics 419 The Helium Atom 424
Multielectron Atoms and the Periodic Table 437 Covalent Bonding 441 Conclusion 448 Problems 448
Scattering 451
The Asymptotic Wave Function and the Differential Cross Section 451
The Bom Approximation 458
An Example of the Bom Approximation: The Yukawa
Potential 463
13.4 The Partial Wave Expansion 465
13.5 Examples of Phase-Shift Analysis 469
13.6 Summary 477 Problems 478
Chapter 14 Photoas and Atoms 483
The Aharonov-Bohm Effect 483
The Hamiltonian for the Electromagnetic Field 488
Quantizing the Radiation Field 493
The Hamiltonian of the Atom and the Electromagnetic Field 501
Time-Dependent Perturbation Theory 504
Fermi’s Golden Rule 513
Spontaneous Emission 518
Cavity Quantum Electrodynamics 526
Higher Order Processes and Feynman Diagrams 530
Problems 533
Appendix A
Electromagnetic Units 539
Appendix B
The Addition of Angular Momenta 545
Appendix C
Dirac Delta Functions 549
Appendix D
Gaussian Integrals 553
Appendix E
The Lagrangian for a Charge q in a Magnetic Field 557
Appendix F
Values of Physical Constants 561
Appendix G
Answers to Selected Problems 563
Index 565

JOHN S. TOWNSEND, Susan and Bruce Worster Professor of Physics at Harvey Mudd College, the science and engineering college of the Claremont Colleges, USA. He received his BS from Duke University, his PhD from Johns Hopkins University, USA, 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, USA. Townsend is also the author of Quantum Physics: A Fundamental Approach to Modern Physics.

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