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Phase Integral Method
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Book Synopsis Phase-Integral Method by : Nanny Fröman
Download or read book Phase-Integral Method written by Nanny Fröman and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Phase-Integral Methods by : John Heading
Download or read book An Introduction to Phase-Integral Methods written by John Heading and published by Courier Corporation. This book was released on 2013-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Physical Problems Solved by the Phase-Integral Method by : Nanny Fröman
Download or read book Physical Problems Solved by the Phase-Integral Method written by Nanny Fröman and published by Cambridge University Press. This book was released on 2002-06-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Phase-Integral Method by : Nanny Fröman
Download or read book Phase-Integral Method written by Nanny Fröman and published by Springer. This book was released on 2011-10-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Phase-integral Methods by : J Heading
Download or read book An Introduction to Phase-integral Methods written by J Heading and published by Hassell Street Press. This book was released on 2021-09-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein
Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Path Integral Methods in Quantum Field Theory by : R. J. Rivers
Download or read book Path Integral Methods in Quantum Field Theory written by R. J. Rivers and published by Cambridge University Press. This book was released on 1988-10-27 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Techniques and Applications of Path Integration by : L. S. Schulman
Download or read book Techniques and Applications of Path Integration written by L. S. Schulman and published by Courier Corporation. This book was released on 2012-10-10 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.
Book Synopsis Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase by : Douglas S. Jones
Download or read book Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase written by Douglas S. Jones and published by . This book was released on 1956 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stark Effect In A Hydrogenic Atom Or Ion: Treated By The Phase-integral Method With Adjoined Papers By A Hokback And P O Froman by : Froman Nanny
Download or read book Stark Effect In A Hydrogenic Atom Or Ion: Treated By The Phase-integral Method With Adjoined Papers By A Hokback And P O Froman written by Froman Nanny and published by World Scientific. This book was released on 2008-03-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrödinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock-Krylov theorem. From this formula one obtains by means of the phase-integral approximation generated from a particular base function non-relativistic formulas for profiles, energies and half-widths of the Stark levels. These formulas are then transformed into formulas expressed in terms of complete elliptic integrals. The formulas thus obtained are used for the calculation of energies and half-widths of 198 different Stark states, which are compared with the corresponding results obtained by other authors with the use of other methods. An analysis of this material indicates that the energy values obtained by the phase-integral method are at least as accurate as those obtained by other methods in more than half of the 198 cases. The book presents one of the most comprehensive asymptotic treatments of the Stark effect in atomic hydrogen that have been published./a
Book Synopsis A Modern Approach to Functional Integration by : John R. Klauder
Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Book Synopsis Phase Transitions by : Moshe Gitterman
Download or read book Phase Transitions written by Moshe Gitterman and published by World Scientific Publishing Company. This book was released on 2013-09-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive review of the theory of phase transitions and its modern applications, based on the five pillars of the modern theory of phase transitions: the Ising model, mean field, scaling, renormalization group and universality. This expanded second edition includes, along with a description of vortices and high temperature superconductivity, a discussion of phase transitions in chemical reactions and moving systems. The book covers the close connection between phase transitions and small world phenomena as well as scale-free systems such as the stock market and the Internet.
Book Synopsis Integral Equation Methods in Scattering Theory by : David Colton
Download or read book Integral Equation Methods in Scattering Theory written by David Colton and published by SIAM. This book was released on 2013-11-15 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rigorous Time Slicing Approach to Feynman Path Integrals by : Daisuke Fujiwara
Download or read book Rigorous Time Slicing Approach to Feynman Path Integrals written by Daisuke Fujiwara and published by Springer. This book was released on 2017-06-24 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved.The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method.This book consists of two parts. Part I is the main part. The time slicing method is performed step by step in detail in Part I. The time interval is divided into small pieces. Corresponding to each division a finite-dimensional integral is constructed following Feynman's famous paper. This finite-dimensional integral is not absolutely convergent. Owing to the assumption of the potential, it is an oscillatory integral. The oscillatory integral techniques developed in the theory of partial differential equations are applied to it. It turns out that the finite-dimensional integral gives a finite definite value. The stationary phase method is applied to it. Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail.Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer. A careful discussion is required to prove the convergence of the approximate sequence as the length of each of the small subintervals tends to 0. For that purpose the book uses the stationary phase method of oscillatory integrals over a space of large dimension, of which the detailed proof is given in Part II of the book. By virtue of this method, the approximate sequence converges to the limit. This proves that the Feynman path integral converges. It turns out that the convergence occurs in a very strong topology. The fact that the limit is the fundamental solution of the Schrödinger equation is proved also by the stationary phase method. The semi-classical asymptotic formula naturally follows from the above discussion.A prerequisite for readers of this book is standard knowledge of functional analysis. Mathematical techniques required here are explained and proved from scratch in Part II, which occupies a large part of the book, because they are considerably different from techniques usually used in treating the Schrödinger equation.
Book Synopsis Integral Methods in Science and Engineering by : Barbara S Bertram
Download or read book Integral Methods in Science and Engineering written by Barbara S Bertram and published by CRC Press. This book was released on 2019-05-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.
Book Synopsis Asymptotic Methods for Integrals by : Nico M Temme
Download or read book Asymptotic Methods for Integrals written by Nico M Temme and published by World Scientific. This book was released on 2014-10-31 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH
Book Synopsis Uniform Stationary Phase Method by : Vladimir Andreevich Borovikov
Download or read book Uniform Stationary Phase Method written by Vladimir Andreevich Borovikov and published by . This book was released on 1994 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph expounds an original asymptotic stationary phase method for the evaluation of integrals of rapidly oscillating functions, which should be beneficial in wave radiation, propagation and diffraction research. It is self-contained, with theory, formulae and tabulated co-efficients.
