Generalization to Absence of Spherical Symmetry p. 48 Scattering by a Uniform Sphere (Mie Theory) p. 48 Calculation of the [characters not

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1 Scattering of Electromagnetic Waves p. 1 Formalism and General Results p. 3 The Maxwell Equations p. 3 Stokes Parameters and Polarization p. 4 Definition of the Stokes Parameters p. 4 Significance of the Parameters p. 6 Partially Polarized Beams p. 8 Stokes Vectors p. 9 Relation to the Density Matrix p. 10 Scattering p. 11 The Scattering Amplitude p. 11 Change to a Reference Plane through a Fixed Direction p. 12 Relation of Circular to Linear Polarization Components in the Scattering Amplitude p. 12 Stokes Vectors of the Scattered Wave p. 13 The Differential Cross Section p. 14 The Density Matrix of the Scattered Wave p. 15 Azimuthal Dependence of Forward and Backward Scattering p. 16 Effects of Rotational or Reflectional Symmetry p. 16 Forward Scattering; the Optical Theorem p. 18 Double Scattering p. 20 Scattering by a Cloud of Many Particles p. 23 Addition of Cross Sections p. 23 Index of Refraction p. 24 More than One Kind of Particle p. 26 Notes and References p. 27 Problems p. 28 Spherically Symmetric Scatterers p. 30 Spherical Harmonics p. 30 Legendre Polynomials p. 30 Associated Legendre Functions p. 31 Spherical Harmonics p. 31 Vector Spherical Harmonics p. 32 Transverse and Longitudinal Vector Spherical Harmonics p. 34 Rotationally Invariant Tensor Functions p. 35 Complex Conjugation Properties p. 36 [theta] and [phi] Components p. 36 The z Axis along r p. 37 Multipole Expansions p. 38 Expansion of a Plane Wave; Spherical Bessel Functions p. 38 Expansion of the Electric Field p. 40 The Magnetic Field p. 41 The [characters not reproducible] Matrix p. 42 The Scattering Amplitude p. 42 The z Axis along k p. 42 Unitarity and Reciprocity p. 44 Energy Conservation and Unitarity p. 44 Phase Shifts p. 45 Time Reversal and Reciprocity p. 46 The Generalized Optical Theorem p. 47

2 Generalization to Absence of Spherical Symmetry p. 48 Scattering by a Uniform Sphere (Mie Theory) p. 48 Calculation of the [characters not reproducible] Matrix p. 48 The Scattering Amplitude p. 50 Notes and References p. 51 Problems p. 52 Limiting Cases and Approximations p. 54 Small Spheres, Not Too Dense (Rayleigh Scattering) p. 54 Low Optical Density, Not Too Large (Rayleigh-Gans; Born Approximation) p. 56 Small Dense Spheres p. 61 Resonance Scattering p. 61 Totally Reflecting Spheres p. 65 Large Diffuse Spheres (Van de Hulst Scattering) p. 66 Forward Scattering p. 66 Small-Angle Scattering p. 69 Large Spheres (Geometrical-Optics Limit) p. 70 Fraunhofer Diffraction p. 71 Nonforward and Nonbackward Scattering; Real Index of Refraction p. 72 Large Diffuse Spheres p. 76 Large Dense Spheres p. 77 Complex Index of Refraction p. 77 The Rainbow p. 78 The Glory p. 82 Grazing Rays (The Watson Method) p. 83 The Watson Transform p. 84 Convergence Questions p. 90 Saddle-Point Integration (The Method of Steepest Descent) p. 94 Notes and References p. 96 Problems p. 96 Miscellaneous p. 98 Other Methods p. 98 Debye Potentials p. 98 The Green's-Function Method p. 100 Causality and Dispersion Relations p. 103 Introduction p. 103 Forward-Dispersion Relations p. 104 Nonforward-Dispersion Relations p. 107 Partial-Wave-Dispersion Relations p. 109 Intensity-Fluctuation Correlations (Hanbury Brown and Twiss Effect) p. 110 Notes and References p. 116 Problems p. 117 Additional References for Part I p. 118 Scattering of Classical Particles p. 119 Particle Scattering in Classical Mechanics p. 121 The Orbit Equation and the Deflection Angle p. 121 The Nonrelativistic Case p. 121 The Relativistic Case p. 123 The Scattering Cross Section p. 124 The Rutherford Cross Section p. 126 Orbiting (Spiral Scattering) p. 127

3 Glory and Rainbow Scattering p. 129 Singular Potentials p. 130 Transformation Between Laboratory and Center-of-Mass Coordinate Systems p. 132 Indentical Particles p. 136 The Inverse Problem p. 137 Notes and References p. 139 Problems p. 140 Quantum Scattering Theory p. 141 Time-Dependent Formal Scattering Theory p. 143 The Schrodinger Equation p. 145 Time Development of State Vectors in the Schrodinger Picture p. 146 The Moller Wave Operator in the Schrodinger Picture p. 151 The S Matrix p. 156 The Interaction Picture p. 158 The Heisenberg Picture p. 160 Scattering into Cones p. 162 Mathematical Questions p. 164 Convergence of Vectors p. 164 Operator Convergence p. 166 Convergences in the Schrodinger Picture p. 169 The Limits in the Interaction Picture p. 171 The Limits in the Heisenberg Picture p. 172 Notes and References p. 172 Problems p. 174 Time-Independent Formal Scattering Theory p. 175 Green's Functions and State Vectors p. 176 The Green's Functions p. 176 The State Vectors p. 178 Expansion of the Green's Functions p. 181 The Wave Operator and the S Matrix p. 182 The Operators [Omega], S, and S' p. 182 The T Matrix p. 183 The K Matrix p. 187 Unitarity and Reciprocity p. 189 Additive Interactions p. 191 Mathematical Questions p. 194 The Spectrum p. 195 Compact Operators p. 198 Hermitian and Unitary Operators p. 200 Analyticity of the Resolvent p. 204 Appendix p. 208 Notes and References p. 208 Problems p. 209 Cross Sections p. 211 General Definition of Differential Cross Sections p. 211 Relativistic Generalization p. 215 Scattering of Incoherent Beams p. 217 The Density Matrix p. 217 Particles with Spin p. 221 The Cross Section and the Density Matrix of the Scattered Wave p. 225

4 Notes and References p. 226 Problems p. 227 Formal Methods of Solution and Approximations p. 228 Perturbation Theory p. 228 The Born Series p. 228 The Born Approximation p. 238 The Distorted-Wave Born Approximation p. 239 Bound States from the Born Approximation p. 240 The Schmidt Process (Quasi Particles) p. 241 The Fredholm Method p. 247 Singularities of an Operator Inverse p. 255 Notes and References p. 257 Problems p. 258 Single-Channel Scattering (Three-Dimensional Analysis in Specific p. 260 Representations) The Scattering Equation in the One-Particle Case p. 260 Preliminaries p. 260 The Coordinate Representation p. 261 The Momentum Representation p. 266 Separable Interactions p. 268 The Scattering Equations in the Two-Particle Case (Elimination of Center-of-Mass p. 270 Motion) Three-Dimensional Analysis of Potential Scattering p. 273 Born Series p. 274 Fredholm Theory p. 277 Scattering Amplitude, Cross Section, and S Matrix p. 282 Dispersion Relations p. 289 An Example (the Yukawa Potential) p. 291 Notes and References p. 295 Problems p. 297 Single-Channel Scattering of Spin 0 Particles, I p. 298 Partial-Wave Expansion p. 298 The S Matrix and Traveling Waves p. 298 The K Matrix and Standing Waves p. 303 Time Delay p. 304 Heuristic Survey of Phase-Shift Behavior p. 305 General Properties p. 305 Discussion of Low-Energy Phase-Shift Behavior p. 306 Variational Approaches p. 318 General Introduction p. 318 The T Matrix, K Matrix, and the Green's Function p. 319 Variational Formulations of the Phase Shift p. 321 The s-wave Scattering Length p. 322 Proof of the Hylleraas-Undheim Theorem p. 326 Notes and References p. 327 Problems p. 328 Single-Channel Scattering of Spin 0 Particles, II p. 331 Rigorous Discussion of s-wave Scattering p. 331 The Regular and Irregular Solutions p. 331 The Jost Function and the Complete Green's Function p. 341

5 The S Matrix p. 350 The Poles of S p. 357 Completeness p. 368 Higher Angular Momenta p. 371 Continuous Angular Momenta p. 380 Singular Potentials p. 389 The Difficulties p. 389 Singular Repulsive Potentials p. 392 An Example p. 394 Notes and References p. 396 General References p. 399 Problems p. 399 The Watson-Regge Method (Complex Angular Momentum) p. 402 The Watson Transform p. 402 Uniqueness of the Interpolation p. 408 Regge Poles p. 410 The Mandelstam Representation p. 412 Notes and References p. 415 Problems p. 416 Examples p. 417 The Zero-Range Potential p. 418 The Repulsive Core p. 419 The Exponential Potential p. 420 The Hulthen Potential p. 421 Potentials of the Yukawa Type p. 422 The Coulomb Potential p. 424 The Pure Coulomb Field p. 424 Coulomb Admixtures p. 431 Bargmann Potentials and Generalizations p. 433 General Procedure p. 433 Special Cases p. 437 Notes and References p. 440 Problems p. 441 Elastic Scattering of Particles with Spin p. 444 Partial-Wave Analysis p. 444 Expansion in j and s p. 444 Amplitudes for Individual Spins p. 450 Unitarity, Reciprocity, Time-Reversal Invariance, and Parity Conservation p. 452 Special Cases p. 457 Cross Sections p. 459 Double Scattering p. 460 Solution of the Coupled Schrodinger Equations p. 461 The Matrix Equation p. 461 Solutions p. 462 Jost Matrix and S Matrix p. 464 Bound States p. 468 Miscellaneous Remarks p. 471 Notes and References p. 472 Problems p. 472 Inelastic Scattering and Reactions (Multichannel Theory), I p. 474

6 Descriptive Introduction p. 474 Time-Dependent Theory p. 477 The Schrodinger Picture p. 477 The Heisenberg Picture p. 482 Two-Hilbert-Space Formulation p. 483 Time-Independent Theory p. 485 Formal Theory p. 485 Distorted-Wave Rearrangement Theory p. 487 Identical Particles p. 488 Large-Distance Behavior of the Two-Cluster Wave Function p. 489 Partial-Wave Analysis p. 492 The Coupled Equations p. 492 The S Matrix p. 494 Rearrangements p. 495 General Scattering Rates p. 495 Formal Resonance Theory p. 500 Appendix p. 508 Notes and References p. 510 Problems p. 513 Inelastic Scattering and Reactions (Multichannel Theory), II p. 514 Analyticity in Many-Channel Problems p. 514 The Coupled Equations p. 514 An Alternative Procedure p. 519 Analyticity Properties p. 521 Bound States p. 526 The Riemann Surface of the Many-Channel S Matrix p. 528 Threshold Effects p. 534 Threshold Branch Points p. 534 Physical Threshold Phenomena; General Arguments p. 538 Details of the Anomaly p. 539 The Threshold Anomaly for Charged Particles p. 544 Examples p. 548 The Square Well p. 548 Potentials of Yukawa Type p. 551 The Wigner-Weisskopf Model p. 553 The Three-Body Problem p. 555 Failure of the Multichannel Method and of the Lippmann-Schwinger Equation p. 555 The Faddeev Method p. 558 Other Methods p. 560 Fredholm Properties and Spurious Solutions p. 563 The Asymptotic Form of Three-Particle Wave Functions p. 565 Angular Momentum Couplings p. 571 The S Matrix p. 579 The Efimov Effect p. 580 Notes and References p. 581 Problems p. 586 Short-Wavelength Approximations p. 588 Introduction p. 588 Diffraction from the Optical Theorem p. 590 The WKB Method p. 591

7 The WKB Phase Shifts p. 591 The Scattering Amplitude p. 594 The Rainbow p. 597 The Glory p. 598 Orbiting (Spiral Scattering) p. 600 The Eikonal Approximation p. 600 The Impulse Approximation p. 605 Notes and References p. 609 Problems p. 611 The Decay of Unstable States p. 612 Qualitative Introduction p. 612 Exponential Decay and Its Limitations p. 614 Multiple Poles of the S Matrix p. 625 Notes and References p. 626 Problems p. 626 The Inverse Scattering Problem p. 629 Introduction p. 629 The Phase of the Amplitude p. 633 The Central Potential Obtained from a Phase Shift p. 637 The Gel'fand-Levitan Equations p. 637 Infinitesimal Variations p. 645 The Marchenko Equation p. 648 The Central Potential Obtained from All Phase Shifts at One Energy p. 650 The Construction Procedure p. 650 Examples p. 657 The Inverse Scattering Problem for Noncentral Potentials p. 659 Introduction p. 659 The Generalized Marchenko Equation p. 659 A Generalized Gel'fand-Levitan Equation p. 665 Potential Obtained from Backscattering p. 666 Notes and References p. 667 Problems p. 670 Bibliography p. 671 Index p. 727 Errata p. 745 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission