UID:
almahu_9947367063802882
Format:
1 online resource (449 p.)
ISBN:
1-282-28886-5
,
9786612288869
,
0-08-095604-1
Series Statement:
Mathematics in science and engineering ; v. 95
Content:
Causality and dispersion relations
Note:
Description based upon print version of record.
,
Front Cover; Causality and Dispersion Relations; Copyright Page; Contents; Preface; Part I: CAUSALITY AND ANALYTICITY; Chapter 1. Causality and Dispersion Relations; 1.1. Introduction; 1.2. The Damped Harmonic Oscillator; 1.3. Causality and Analyticity; 1.4. Light Propagation in a Dielectric Medium; 1.5. Physical Origin of Dispersion Relations; 1.6. Titchmarsh's Theorem; 1.7. Subtractions; 1.8. Dispersion Relations and Distributions; 1.9. The Kramers-Kronig Relation; 1.10. The Optical Theorem; References; Chapter 2. Partial-Wave Dispersion Relations; 2.1. Introduction
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2.2. Classical Field: s-Wave Scattering2.3. The Causality Condition; 2.4. Analytic Continuation to I _; 2.5. Product Expansion; 2.6. Extension to Higher Angular Momenta; 2.7. Nonrelativistic Quantum Scattering; 2.8. The Schützer-Tiomno Causality Condition; 2.9. Van Kampen's Causality Condition; 2.10. The R-Function; 2.11. Wigner's Causal Inequality; 2.12. Completeness; References; Chapter 3. Dispersion Relations for the Total Scattering Amplitude; 3.1. Introduction; 3.2. Dispersion Relations for Fixed Scattering Angle; 3.3. Dispersion Relations for Fixed Momentum Transfer
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3.4. Fxtension to Nonrelativistic Quantum ScatteringReferences; Chapter 4. Physical Interpretation of S-Matrix Singularities; 4.1. Introduction; 4.2. Effects on the Cross Section; 4.3. Complex Poles and Unstable States; 4.4. Vibrating String and Oscillator; 4.5. The Transient-Mode Propagator for the Schrüdinger Equation; 4.6. Application to an Explicit Model; References; Part II: POTENTIAL SCATTERING; Chapter 5. Analytic Properties of Partial-Wave Amplitudes; 5.1. Introduction; 5.2. The Jost Function; 5.3. Analytic Properties of the Jost Function; 5.4. The Singularities of the S-Function
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5.5. Cutoff Potentials5.6. An Example: Square Well or Barrier; 5.7. M ittag-Leffler and Transient-Mode Expansions; 5.8. Extension to Higher Angular Momenta; References; Chapter 6. Analytic Properties of the Total Amplitude; 6.1. Introduction; 6.2. The Resolvent Operator in Banach Space; 6.3. Analytic Properties of the Total Scattering Amplitude; 6.4. High-Energy Behavior of the Scattering Amplitude; 6.5. Dispersion Relations for Fixed Momentum Transfer; 6.6. Analyticity in Momentum Transfer and Finite Range of the Interaction; References; Chapter 7. Regge Poles; 7.1. Introduction
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A2. The Space D and Schwartz Distributions
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English
Additional Edition:
ISBN 0-12-523050-8
Language:
English
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