Lectures in Scattering Theory

PrefaceChapter 1. Quantum-Mechanical Description and Representations 1.1. Quantum-Mechanical Description of Physical Systems 1.2. The Schrödinger Representation 1.3. The Heisenberg Representation 1.4. The Interaction Representation ProblemsChapter 2. The Scattering Matrix and Transition Probability 2.1. The Scattering Matrix 2.2. The Time-Shift Operator in the Interaction Representation 2.3. Integrals of Motion and Diagonalization of the S-Matrix 2.4. The Transition Probability Per Unit Time 2.5. An Integral Equation for the T-Matrix 2.6. Transformation of the Scattering Matrix. Cross-Sections ProblemsChapter 3. Stationary Scattering Theory 3.1. The Scattering Amplitude 3.2. The Lippmann-Schwinger Equation 3.3. The Relation between the Scattering Amplitude and the Transition Matrix 3.4. Inelastic Scattering and Reactions 3.5. The Born Approximation ProblemsChapter 4. Wave Function of a Particle in an External Field 4.1. Scattering in a Central Field. Expansion in Partial Waves 4.2. The Rectangular Potential Well 4.3. The Coulomb Field ProblemsChapter 5. The Optical Theorem 5.1. The Relation between the Total Cross-Section and the Elastic Scattering Amplitude 5.2. The Unitarity Relation for the Elastic Scattering Amplitude ProblemChapter 6. Time Reversal and the Reciprocity Theorem 6.1. Transformation of the Wave Functions and Operators on Time Reversal 6.2. The Time-Reversal Operator for Specific Systems 6.3. The Time-Reversed Wave Function 6.4. The Reciprocity Theorem and Detailed Balance ProblemsChapter 7. Analytic Properties of the Scattering Matrix 7.1. Analytic Properties of the Radial Wave Functions 7.2. The Case of Non-Zero Angular Momenta 7.3. Zeros of the Jost Function and Bound States 7.4. The Symmetry and Location of the Scattering Matrix Singularities in the Complex Plane 7.5. Bound States and Redundant Zeros 7.6. Quasi-Stationary States and Resonances 7.7. Virtual States 7.8. The Scattering Matrix in the Case of a Rectangular Potential Well ProblemsChapter 8. Dispersion Relations 8.1. Integral Representations of the Jost Functions 8.2. Levinson's Theorem 8.3. The Complex Energy Surface 8.4. Analyticity of the Scattering Matrix and the Causality Principle 8.5. Dispersion Relations for the Scattering AmplitudeChapter 9. Complex Angular Momenta 9.1. Analytic Properties of the Scattering Matrix in the Complex Angular Momentum Plane 9.2. Poles of the Scattering Matrix in the Complex Angular Momentum Plane 9.3. Asymptotic Behaviour of the Scattering Amplitude when cos ¿ ¿ 8 ProblemsChapter 10. Separable Representation of the Scattering Amplitude 10.1. The Scattering Amplitude off the Energy Surface 10.2. The Hilbert-Schmidt Expansion for the Scattering Amplitude 10.3. Properties of the Eigenvalues and Eigenfunctions of the Kernel of the Lippmann-Schwinger Equation ProblemsChapter 11. Scattering in a Three-Particle System 11.1. The Faddeev Equations 11.2. Positions and Momenta in a Three-Particle System 11.3. The Momentum Representation 11.4. Expansion in Partial Waves 11.5. Separable Expansion of the Two-Particle T-Matrix and Reduction of the Faddeev Integral Equations to One-Dimensional Form ProblemChapter 12. Scattering of Particles with Spin 12.1. The Spin Wave Function and Density Matrix 12.2. Expansion of the Density Matrix in Spin-Tensors 12.3. The Scattering Amplitude of Particles with Spin 12.4. Coupling of Spin and Orbital Angular Momenta and Diagonalization of the S-Matrix 12.5. Scattering of a Spin-1/2 Particle by a Spinless Particle 12.6. Scattering of a Spin-1 Particle by a Spinless Particle Problems AppendixBibliographyIndex