《Collision theory Goldberger》求取 ⇩

1.INTRODUCTION1

1.1The Principles of Quantum Mechanics1

1.2 Some Specific Operators9

1.3 Eigenstates of a Free Particle16

1.4 Relativistic Quantum Mechanics21

2.SYMMETRY OPERATIONS ON THE SCHRODINGER EQUATION32

2.1Translations of Coordinates32

2.2 Coordinate Rotations36

2.3 Coordinate Reflections40

2.4 Charge Conjugation41

2.5 Displacement in Time44

2.6 Time Reversal Invariance51

3.THE DESCRIPTION OF SCATTERING PROCESSES58

3.1Preparation of the Initial State59

3.2 Integration of the Schrodinger Equation for Scattering Processes67

3.3 Evaluation of the Scattering Cross Section76

3.4 Physical Interpretations of ψ(t)95

4.FURTHER DESCRIPTION OF SCATTERING PROCESSES111

4.1Description of the Channels of a Reaction111

4.2 Wave Function Symmetrization for Systems of Identical Particles119

4.3 Symmetrization of the Wave Packet States for a Scattering Interaction133

4.4 Evaluation of the Scattering Cross Section141

4.5 Examples148

4.6 Further Description and Simplification of the Matrix Elements of g169

5.FORMAL SCATTERING THEORY173

5.1Limiting Process and Transition Probabilities174

5.2 The S-Matrix and Further Formal Theory186

5.3 Integral Equations for the Determination of the S-Matrix197

5.4 Scattering from Two Potentials202

5.5 The S-Matrix and the Interaction Representation209

5.6 The Reaction Matrix and the Heitler Integral Equation215

5.7 Application to Quantum Field Theory218

6.THE TWO-BODY PROBLEM WITH CENTRAL FORCES221

6.1Coordinate Transformations from the Laboratory to the Barycentric Frame of Reference221

6.2 Partial Wave Analysis and the Scattering Phase Shifts226

6.3 Nonrelativistic Potential Scattering243

6.4 Examples252

6.5 Analytic Properties of Partial Wave Amplitudes269

6.6 Effective-Range Theory286

6.7 Approximation Methods299

6.8 The Potential Scattering of Relativistic Particles339

7.SCATTERING BY NONCENTRAL FORCES344

7.1Kinematical Description of Scattering by Noncentral Forces345

7.2 Application to the Scattering of Spin Zero by Spin One-Half Particles358

7.3 Scattering Reactions372

7.4 The Scattering of Two Spin One-Half Particles384

7.5 The Density Matrix and the Scattering of Polarized Particles398

7.6 The Solution of the Dirac Equation in a Central Field420

8.THE LIFETIME AND DECAY OF VIRTUAL STATES424

8.1Stationary State Perturbation Theory425

8.2 The Decay of a Prepared State431

8.3 Examples of the Decay of a Prepared State460

8.4 Preparation of an Unstable State by Scattering Interactions474

8.5 General Theory of the Lifetime of Scattering States485

8.6 The General Theory of Resonant Scattering498

9.MISCELLANEOUS APPLICATIONS510

9.1Relativistic Description of the Scattering of Spin One-Half Particles by a Force Center510

9.2 The Scattering and Photoproduction of Pi-Mesons from Nucleons518

9.3 The Theory of Final State Interactions540

9.4 Applications of Formal Scattering Theory to Field Theory553

10.INTRODUCTION TO DISPERSION THEORY557

10.1Historical Background557

10.2 Formal Considerations563

10.3 Nonrelativistic Theory567

10.4 Dispersion Relations in Nonrelativistic Theory585

10.5 Two-Dimensional Representation598

10.6 Dispersion Relations in Relativistic Field Theory621

11.SCATTERING BY SYSTEMS OF BOUND PARTICLES679

11.1Scattering from a Single Weakly Bound Particle680

11.2 Scattering by a Small System of Bound Scatterers708

11.3 Multiple Scattering by a System of Bound Particles749

11.4 Use of a Pseudopotential to Describe Elastic Scattering780

11.5 Coherence and Incoherence in Multiple Scattering Phenomena804

11.6 Deuteron Stripping and Pick-Up Reactions833

11.7 The Scattering of Charged Particles by Atoms850

APPENDICES867

ATable of Wigner Coefficients867

B Collisions Involving Three Incident Particles868

C Completeness and Orthogonality of Channel States872

D Computational Methods for Scattering at Low Energy879

E The Jacob-Wick Expansion of the Scattering Matrix882

F Evaluation of the Amplitude for Nucleon-Nuclcon Scattering in Terms of Phase Shifts899

G.1 Nonrelativistic Dispersion Relations for Combinations of Ordinary and Exchange Potentials903

G.2 Solution of a Class of Integral Equations908

INDEX913