Phase-Integral Method
Phase-Integral Method

Author: Nanny Fröman

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 258

ISBN-13: 1461223423

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The result of two decades spent developing and refining the phase-integral method to a high level of precision, the authors have applied this method to problems in various fields of theoretical physics. The problems treated are of a mathematical nature, but have important physical applications. This book will thus be of great use to research workers in various branches of theoretical physics, where the problems can be reduced to one-dimensional second-order differential equations of the Schrödinger type for which phase-integral solutions are required. Includes contributions from notable scientists who have already made use of the authors'technique.

An Introduction to Phase-Integral Methods
An Introduction to Phase-Integral Methods

Author: John Heading

Publisher: Courier Corporation

Published: 2013-06-03

Total Pages: 178

ISBN-13: 0486316297

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Introductory treatment steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students. Topics include Stokes phenomenon, one and two transition points, applications. 1962 edition.

Physical Problems Solved by the Phase-Integral Method
Physical Problems Solved by the Phase-Integral Method

Author: Nanny Fröman

Publisher: Cambridge University Press

Published: 2002-06-13

Total Pages: 230

ISBN-13: 1139434322

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This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

An Introduction to Phase-Integral Methods
An Introduction to Phase-Integral Methods

Author: John Heading

Publisher: Courier Corporation

Published: 2013-01-01

Total Pages: 178

ISBN-13: 0486497429

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The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.

Asymptotic Expansions of Integrals
Asymptotic Expansions of Integrals

Author: Norman Bleistein

Publisher: Courier Corporation

Published: 1986-01-01

Total Pages: 453

ISBN-13: 0486650820

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Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Integral Equation Methods in Scattering Theory
Integral Equation Methods in Scattering Theory

Author: David Colton

Publisher: SIAM

Published: 2013-11-15

Total Pages: 286

ISBN-13: 1611973155

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This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

Path Integral Methods in Quantum Field Theory
Path Integral Methods in Quantum Field Theory

Author: R. J. Rivers

Publisher: Cambridge University Press

Published: 1988-10-27

Total Pages: 356

ISBN-13: 9780521368704

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The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and quantum field theory.

Numerical Methods for Two-phase Incompressible Flows
Numerical Methods for Two-phase Incompressible Flows

Author: Sven Gross

Publisher: Springer Science & Business Media

Published: 2011-04-26

Total Pages: 487

ISBN-13: 3642196861

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This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.