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

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

[PDF eBook eTextbook]

• 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

CHAPTER 1

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

CHAPTER 2

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

CHAPTER 3

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

CHAPTER 4

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

CHAPTER 5

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

CHAPTER 6

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

CHAPTER 7

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

CHAPTER 10

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

CHAPTER 11

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

CHAPTER 12

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

CHAPTER 13

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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