Sweet: An MM Romance Thriller

Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.>Provides clear and accessible explanations of the foundations of quantum mechanics, using an attractive and informal style>It is thorough, with an appropriate amount of mathematical rigor and a good variety of examples and problems>Students emerge with a confident understanding of what the theory says and how to apply it, a solid foundation for more advanced work, and an appreciation for one of the greatest products of the human mind Half-title page 2 Title page 3 Imprints page 4 Contents 6 Preface 11 Part I Theory 14 1 The Wave Function 15 1.1 The Schrödinger Equation 16 1.2 The Statistical Interpretation 17 1.3 Probability 21 1.3.1 Discrete Variables 22 1.3.2 Continuous Variables 26 1.4 Normalization 29 1.5 Momentum 32 1.6 The Uncertainty Principle 35 Further Problems on Chapter 1 36 2 Time-Independent Schrödinger Equation 42 2.1 Stationary States 43 2.2 The Infinite Square Well 49 2.3 The Harmonic Oscillator 57 2.3.1 Algebraic Method 59 2.3.2 Analytic Method 67 2.4 The Free Particle 74 2.5 The Delta-Function Potential 81 2.5.1 Bound States and Scattering States 82 2.5.2 The Delta-Function Well 85 2.6 The Finite Square Well 93 Further Problems on Chapter 2 99 3 Formalism 118 3.1 Hilbert Space 119 3.2 Observables 122 3.2.1 Hermitian Operators 123 3.2.2 Determinate States 125 3.3 Eigenfunctions of a Hermitian Operator 127 3.3.1 Discrete Spectra 128 3.3.2 Continuous Spectra 130 3.4 Generalized Statistical Interpretation 133 3.5 The Uncertainty Principle 137 3.5.1 Proof of the Generalized Uncertainty Principle 138 3.5.2 The Minimum-Uncertainty Wave Packet 141 3.5.3 The Energy-Time Uncertainty Principle 142 3.6 Vectors and Operators 147 3.6.1 Bases in Hilbert Space 148 3.6.2 Dirac Notation 152 3.6.3 Changing Bases in Dirac Notation 157 Further Problems on Chapter 3 159 4 Quantum Mechanics in Three Dimensions 170 4.1 The Schröger Equation 171 4.1.1 Spherical Coordinates 174 4.1.2 The Angular Equation 176 4.1.3 The Radial Equation 180 4.2 The Hydrogen Atom 185 4.2.1 The Radial Wave Function 187 4.2.2 The Spectrum of Hydrogen 198 4.3 Angular Momentum 201 4.3.1 Eigenvalues 202 4.3.2 Eigenfunctions 208 4.4 Spin 212 4.4.1 Spin 1/2 214 4.4.2 Electron in a Magnetic Field 219 4.4.3 Addition of Angular Momenta 223 4.5 Electromagnetic Interactions 228 4.5.1 Minimal Coupling 229 4.5.2 The Aharonov?Bohm Effect 231 Further Problems on Chapter 4 235 5 Identical Particles 251 5.1 Two-Particle Systems 252 5.1.1 Bosons and Fermions 256 5.1.2 Exchange Forces 259 5.1.3 Spin 263 5.1.4 Generalized Symmetrization Principle 264 5.2 Atoms 267 5.2.1 Helium 268 5.2.2 The Periodic Table 271 5.3 Solids 275 5.3.1 The Free Electron Gas 276 5.3.2 Band Structure 281 Further Problems on Chapter 5 285 6 Symmetries & Conservation Laws 294 6.1 Introduction 295 6.1.1 Transformations in Space 296 6.2 The Translation Operator 298 6.2.1 How Operators Transform 299 6.2.2 Translational Symmetry 302 6.3 Conservation Laws 307 6.4 Parity 308 6.4.1 Parity in One Dimension 309 6.4.2 Parity in Three Dimensions 312 6.4.3 Parity Selection Rules 314 6.5 Rotational Symmetry 316 6.5.1 Rotations About the z Axis 317 6.5.2 Rotations in Three Dimensions 319 6.6 Degeneracy 323 6.7 Rotational Selection Rules 326 6.7.1 Selection Rules for Scalar Operators 327 6.7.2 Selection Rules for Vector Operators 331 6.8 Translations in Time 336 6.8.1 The Heisenberg Picture 338 6.8.2 Time-Translation Invariance 341 Further Problems on Chapter 6 343 Part II Applications 354 7 Time-Independent Perturbation Theory 355 7.1 Nondegenerate Perturbation Theory 356 7.1.1 General Formulation 357 7.1.2 First-Order Theory 359 7.1.3 Second-Order Energies 363 7.2 Degenerate Perturbation Theory 366 7.2.1 Two-Fold Degeneracy 367 7.2.2 “Good” States 373 7.2.3 Higher-Order Degeneracy 376 7.3 The Fine Structure of Hydrogen 378 7.3.1 The Relativistic Correction 380 7.3.2 Spin-Orbit Coupling 384 7.4 The Zeeman Effect 389 7.4.1 Weak-Field Zeeman Effect 390 7.4.2 Strong-Field Zeeman Effect 393 7.4.3 Intermediate-Field Zeeman Effect 395 7.5 Hyperfine Splitting in Hydrogen 398 Further Problems on Chapter 7 400 8 The Varitional Principle 417 8.1 Theory 418 8.2 The Ground State of Helium 424 8.3 The Hydrogen Molecule Ion 429 8.4 The Hydrogen Molecule 434 Further Problems on Chapter 8 439 9 The WKB Approximation 449 9.1 The “Classical” Region 450 9.2 Tunneling 455 9.3 The Connection Formulas 460 Further Problems on Chapter 9 468 10 Scattering 475 10.1 Introduction 476 10.1.1 Classical Scattering Theory 477 10.1.2 Quantum Scattering Theory 481 10.2 Partial Wave Analysis 483 10.2.1 Formalism 484 10.2.2 Strategy 487 10.3 Phase Shifts 490 10.4 The Born Approximation 493 10.4.1 Integral Form of the Schrödinger Equation 494 10.4.2 The First Born Approximation 498 10.4.3 The Born Series 502 Further Problems on Chapter 10 503 11 Quantum Dynamics 510 11.1 Two-Level Systems 512 11.1.1 The Perturbed System 513 11.1.2 Time-Dependent Perturbation Theory 516 11.1.3 Sinusoidal Perturbations 520 11.2 Emission and Absorption of Radiation 523 11.2.1 Electromagnetic Waves 524 11.2.2 Absorption, Stimulated Emission, and Spontaneous Emission 525 11.2.3 Incoherent Perturbations 527 11.3 Spontaneous Emission 529 11.3.1 Einstein’s A and B Coefficients 530 11.3.2 The Lifetime of an Excited State 533 11.3.3 Selection Rules 536 11.4 Fermi’s Golden Rule 538 11.5 The Adiabatic Approximation 542 11.5.1 Adiabatic Processes 543 11.5.2 The Adiabatic Theorem 546 Further Problems on Chapter 11 550 12 Afterword 566 12.1 The EPR Paradox 567 12.2 Bell’s Theorem 569 12.3 Mixed States and the Density Matrix 575 12.3.1 Pure States 576 12.3.2 Mixed States 579 12.3.3 Subsystems 582 12.4 The No-Clone Theorem 583 12.5 Schrödinger’s Cat 585 Appendix Linear Algebra 589 A.1 Vectors 590 A.2 Inner Products 593 A.3 Matrices 596 A.4 Changing Bases 601 A.5 Eigenvectors and Eigenvalues 604 A.6 Hermitian Transformations 612 Index 616 Theory, The Wave Function -- Time-independent Schrödinger Equation -- Formalism -- Quantum Mechanics In Three Dimensions -- Identical Particles -- Applications. Time-independent Perturbation Theory -- The Variational Principle -- The Wkb Approximation -- Time-dependent Perturbation Theory -- The Adiabatic Approximation -- Scattering -- Appendix: Linear Algebra. David J. Griffiths And Darrell F. Schroeter. Schrödinger Equation. Includes Bibliographical References And Index.