Greens Functions And Ordered Exponentials
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| Author | : H. M. Fried |
| Publisher | : Cambridge University Press |
| Total Pages | : 183 |
| Release | : 2002-10-10 |
| Genre | : Science |
| ISBN | : 1139433059 |
This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
| Author | : Antonios Gonis |
| Publisher | : North Holland |
| Total Pages | : 726 |
| Release | : 1992 |
| Genre | : Science |
| ISBN | : |
The book presents an exposition of Green functions and multiple scattering theory (MST) as presently used in the study of the electronic structure of matter. Ordered, as well as substitutionally disordered systems are discussed. This volume deals with both a tight binding approach to and a first-principles formulation of Green functions and multiple scattering theory. It includes extended discussions on such topics as the coherent potential approximation (CPA), and the use of full cell potentials in applications of MST to the calculation of electronic structure of solids. Special emphasis is given to the derivation of formulae within the angular momentum representation, as well as to problems. The book contains a collection of problems of particular interest to students.
| Author | : Alberto Cabada |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 180 |
| Release | : 2013-11-29 |
| Genre | : Mathematics |
| ISBN | : 1461495067 |
This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
| Author | : Dean G. Duffy |
| Publisher | : CRC Press |
| Total Pages | : 461 |
| Release | : 2001-05-31 |
| Genre | : Mathematics |
| ISBN | : 1420034790 |
Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's
| Author | : Yuri A. Melnikov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 448 |
| Release | : 2012-04-02 |
| Genre | : Mathematics |
| ISBN | : 3110253399 |
Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
| Author | : Michael D. Greenberg |
| Publisher | : Prentice Hall |
| Total Pages | : 162 |
| Release | : 1971 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Yuri A. Melnikov |
| Publisher | : Springer |
| Total Pages | : 211 |
| Release | : 2017-05-08 |
| Genre | : Mathematics |
| ISBN | : 3319572431 |
This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.
| Author | : G. Rickayzen |
| Publisher | : Courier Corporation |
| Total Pages | : 370 |
| Release | : 2013-05-22 |
| Genre | : Science |
| ISBN | : 0486499847 |
"Green's functions, named for the mathematician who developed them in the 1830s, possess applications in many areas of physics. This volume presents the basic theoretical formulation, followed by specific applications that include transport coefficients of a metal, the Coulomb gas, Fermi liquids, electrons and phonons, superconductivity, superfluidity, and magnetism. 1984 edition"--
| Author | : Gabriel Barton |
| Publisher | : Oxford University Press |
| Total Pages | : 484 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : 9780198519980 |
This text takes the student with a background in undergraduate physics and mathematics towards the skills and insights needed for graduate work in theoretical physics. The author uses Green's functions to explore the physics of potentials, diffusion, and waves. These are important phenomena in their own right, but this study of the partial differential equations describing them also prepares the student for more advanced applications in many-body physics and field theory. Calculations are carried through in enough detail for self-study, and case histories illustrate the interplay between physical insight and mathematical formalism. The aim is to develop the habit of dialogue with the equations and the craftsmanship this fosters in tackling the problem. The book is based on the author's extensive teaching experience.
| Author | : Michael D. Greenberg |
| Publisher | : Courier Dover Publications |
| Total Pages | : 164 |
| Release | : 2015-08-19 |
| Genre | : Mathematics |
| ISBN | : 0486797961 |
In addition to coverage of Green's function, this concise introductory treatment examines boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. Suitable for undergraduate and graduate students. 1971 edition.
