The Padé approximant in theoretical physics

• Main Authors: Baker, George A. (George Allen), Gammel, John L.
• Format: eBook Book
• Language: English
• Published: New York Academic Press 1970; Elsevier Science & Technology
• Edition: 1
• Subjects: Mathematical physics; Padé approximant
• ISBN: 0120748509; 9780120748501

Table of Contents:

• Chapter 7. Hilbert Space and the Padé Approximant -- I. Introduction -- II. Extended Series of Stieltjes -- III. Symmetric Operators and the Padé Approximant -- IV. Method of Moments -- V. Discussion -- References -- Chapter 8. The Connection of Padé Approximants with Stationary Variational Principles and the Convergence of Certain Padé Approximants -- I. Introduction -- II. Derivation of Padé Approximants from Stationary Variational Principles -- III. Convergence of Padé Approximants -- IV. The Convergence of Padé Approximants to Convergent Power Series -- References -- Chapter 9. Approximate N/D Solutions Using Padé Approximants -- I. Introduction -- II. Method -- III. Proof of Unitarity and Convergence -- IV. Discussion -- References -- Chapter 10. The Solution of the N/D Equations Using the Padé Approximant Method -- I. Introduction -- II. The Integral Equations for Nand D and Their Approximate Solution -- III. Convergent Sequences of Approximate Solutions to the N/D Equations -- IV. The ρ Bootstrap and Related Amplitudes -- References -- Chpater 11. Padé Approximants as a Computational Tool for Solving the Schrödinger and Bethe-Salpeter Equations -- I. Introduction -- II. Basic Philosophy and a Simple Example -- III. Rational-Fraction Fitting -- IV. Two-Channel Nonrelativistic Scattering -- V. Bethe-Salpeter Equation -- VI. Three-Body Scattering -- References -- Chapter 12. Solution of the Bethe-Salpeter Equation by Means of Padé Approximants -- I. Introduction -- II. The Integral Equations -- III. The Numerical Method -- IV. Results and Discussion -- Appendix A -- Appendix B -- References -- Chapter 13. Application of the Padé Approximant to a Coupled Channel Problem: Meson-Baryon Scattering -- I. Introduction -- II. The Padé Approximant to the Scattering Amplitude in the Case of Coupled Channel Potential Models
• Front Cover -- The Padé Approximant in Theoretical Physics -- Copyright Page -- Contents -- List of Contributors -- Preface -- Chapter 1. The Padé Approximant Method and Some Related Generalizations -- I. Introduction -- II. The Theory of the Padé Approximant Method -- III. Generalized Approximation Procedures -- IV. Applications -- References -- Chapter 2. Application of Padé Approximants to Dispersion Force and Optical Polarizability Computations -- I. Introduction -- II. Formalism -- III. Computation Procedures -- IV. Applications -- V. Comparisions with Related Methods -- VI. Concluding Remarks -- References -- Chapter 3. Bounds for Averages Using Moment Constraints -- I. Introduction -- II. The Moments Problem -- III. Applications -- IV. Conclusion -- Appendix A -- Appendix B -- References -- Chapter 4. Turbulent Diffusion: Evaluation of Primitive and Renormalized Perturbation Series by Padé Approximants and by Expansion of Stieltjes Transforms into Contributions from Continuous Orthogonal Functions -- I. Introduction -- II. Continuous Orthogonal Expansion of Stieltjes Transforms -- III. Examples Comparing Continuous Orthogonal Expansion and Padé Approximants -- IV. Diffusion by a Random Velocity Field -- V. Perturbation Expansions for the Diffusion Problem -- VI. Approximants to the Primitive Perturbation Expansions -- VII. Approximants to the Irreducible Expansion References -- References -- Chapter 5. Padé Approximants and Linear Integral Equations -- I. Introduction -- II. Properties of Linear Integral Equations -- III. Integral Equations and Padé Approximants -- IV. The Integral Equation for Potential Scattering References -- References -- Chapter 6. Series of Derivatives of δ-Functions -- I. Introduction -- II. An Example -- III. Expressions for g(k) -- IV. Approximants to g(k) -- V. Conclusions -- References
• III. Formal Preliminaries to the Results -- IV. Results for the (3, 3) State (π+ -p and K+ - Σ+ Elastic Scatterings and Reaction) -- V. Study of a Potential Model -- References -- Chapter 14: The Padé Approximant in the Nucleon-Nucleon System -- I. Introduction -- II. The Padé Approximant in Scattering Theory -- III. The Nucleon-Nucleon System -- IV. The Padé Approximant for N-N Scattering -- V. Results -- VI. Summary -- References -- Author Index -- Subject Index