Scattering Theory

PrefaceChapter I. Introduction 1. The Dynamic Approach 2. Scattering Theory Formulated in Terms of Representation Theory 3. A Semigroup of Operators Related to the Scattering Matrix 4. The Form of the Scattering Matrix 5. A Simple Example 6. Scattering Theory for Transport Phenomena 7. Notes and RemarksChapter II. Representation Theory and the Scattering Operator 1. The Discrete Case 2. The Scattering Operator in the Discrete Case 3. The Continuous Case 4. The Scattering Operator in the Continuous Case 5. Notes and RemarksChapter III. A Semigroup of Operators Related to the Scattering Matrix 1. The Related Semigroups 2. On Semigroups of Contraction Operators 3. Spectral Theory 4. A Spectral Mapping Theorem 5. Applications of the Spectral Theory 6. Equivalent Incoming and Outgoing Representations 7. Notes and RemarksChapter IV. The Translation Representation for the Solution of the Wave Equation in Free Space 1. The Hilbert Space H0 and the Group {U0(t)} 2. Spectral and Translation Representations of {U0(t)} 3. The Operator # Extended to Distributions 4. Translation Representation for Outgoing and Incoming Data with Infinite Energy 5. Notes and RemarksChapter V. The Solution of the Wave Equation in an Exterior Domain 1. The Hilbert Space H and the Group {U(t)} 2 . Energy Decay and Translation Representations 3 . The Semigroup {Z(t)} 4 . The Relation between the Semigroup {Z(t) ) and the Solutions of the Reduced Wave Equation 5 . The Scattering Matrix 6 . Notes and RemarksChapter VI. Symmetric Hyperbolic Systems, the Acoustic Equation with an Indefinite Energy Form, and the Schrödinger Equation Part 1. Symmetric Hyperbolic Systems 1. Translation Representation in Free Space 2. Solutions of Hyperbolic Systems in an Exterior Domain Part 2. The Acoustic Equation with an Indefinite Energy Form and the Schrödinger Equation 3 . Scattering for the Acoustic Equation with an Indefinite Energy Form 4 . The Schrödinger Scattering Matrix 5 . Notes and RemarksAppendix 1. Semigroups of OperatorsAppendix 2. Energy DecayAppendix 3. Energy Decay for Star-Shaped ObstaclesAppendix 4 . Scattering Theory for Maxwell's EquationsReferencesIndex