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Asymptotic Methods For Wave And Quantum Problems
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Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : M. V. Karasev
Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : Mikhail Vladimirovich Karasev
Download or read book Asymptotic Methods for Wave and Quantum Problems written by Mikhail Vladimirovich Karasev and published by . This book was released on 2003 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approxi.
Book Synopsis Asymptotic Methods in Quantum Mechanics by : S.H. Patil
Download or read book Asymptotic Methods in Quantum Mechanics written by S.H. Patil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.
Book Synopsis Asymptotic Methods in Quantum Mechanics by : S H Patil
Download or read book Asymptotic Methods in Quantum Mechanics written by S H Patil and published by . This book was released on 2000-04-26 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some general properties of wave functions, with an emphasis on their asymptotic behaviour. The asymptotic region is particularly important since it is the wave function in the outer region of an atom, a molecule or a nucleus, which is sensitive to external interaction. An analysis of these properties helps in constructing simple and compact wave functions and in developing a broad understanding of different aspects of the quantum mechanics of many-particle systems. As applications, wave functions with correct asymptotic forms are used to generate a large data base for susceptibilities, polarizabilities, interatomic potentials, and nuclear densities.
Book Synopsis Short-Wavelength Diffraction Theory by : Vasili M. Babic
Download or read book Short-Wavelength Diffraction Theory written by Vasili M. Babic and published by Springer. This book was released on 2011-12-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.
Book Synopsis Asymptotic Wave Theory by : Maurice Roseau
Download or read book Asymptotic Wave Theory written by Maurice Roseau and published by Elsevier. This book was released on 2012-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory. It describes techniques such as Fourier-Laplace transforms, operational calculus, special functions, and asymptotic methods. It also discusses applications to the wave equation, the elements of scattering matrix theory, problems related to the wave equation, and diffraction. Organized into eight chapters, this volume begins with an overview of the Fourier-Laplace integral, the Mellin transform, and special functions such as the gamma function and the Bessel functions. It then considers wave propagation, with emphasis on representations of plane, cylindrical or spherical waves. It methodically introduces the reader to the reflexion and refraction of a plane wave at the interface between two homogeneous media, the asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity, and the asymptotic behavior of the Laplace transform. The book also examines the method of steepest descent, the asymptotic representation of Hankel's function of large order, and the scattering matrix theory. The remaining chapters focus on problems of flow in open channels, the propagation of elastic waves within a layered spherical body, and some problems in water wave theory. This book is a valuable resource for mechanics and students of applied mathematics and mechanics.
Book Synopsis Asymptotic Methods in Equations of Mathematical Physics by : B Vainberg
Download or read book Asymptotic Methods in Equations of Mathematical Physics written by B Vainberg and published by CRC Press. This book was released on 1989-02-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Introduction to Asymptotic Methods by : David Y. Gao
Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Book Synopsis Short-Wavelength Diffraction Theory by : Vasili M. Babic
Download or read book Short-Wavelength Diffraction Theory written by Vasili M. Babic and published by Springer. This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.
Book Synopsis Waves and Boundary Problems by : Sergey G. Glebov
Download or read book Waves and Boundary Problems written by Sergey G. Glebov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.
Book Synopsis Asymptotic Methods in Short-wavelength Diffraction Theory by : V. M. Babich
Download or read book Asymptotic Methods in Short-wavelength Diffraction Theory written by V. M. Babich and published by Alpha Science International, Limited. This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to modern approaches of a high-frequency technique in diffraction theory, Asymptotic Methods in Short-Wavelength Diffraction Theory outlines a variety of crucial topics. The book considers a multitude of matters, ranging from the ray method to the theory of high-frequency whispering-gallery waves alongside the reviewing and reflecting on recent results from the literature dealing with localized asymptotic solutions and uniform representation of a high-frequency wave-field. The book serves as an exclusive address to experts on electromagnetics, seismology and acoustics as well as to mathematicians interested in modern approaches of mathematical physics.
Book Synopsis Asymptotic Methods in Nonlinear Wave Theory by : Alan Jeffrey
Download or read book Asymptotic Methods in Nonlinear Wave Theory written by Alan Jeffrey and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Methods in Mechanics by : Rmi Vaillancourt
Download or read book Asymptotic Methods in Mechanics written by Rmi Vaillancourt and published by American Mathematical Soc.. This book was released on 1993-12-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
Book Synopsis Semi-Classical Approximation in Quantum Mechanics by : Victor P. Maslov
Download or read book Semi-Classical Approximation in Quantum Mechanics written by Victor P. Maslov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M. Tsidilin for his valuable comments. THE AUTHORS IX INTRODUCTION 1. Various problems of mathematical and theoretical physics involve partial differential equations with a small parameter at the highest derivative terms. For constructing approximate solutions of these equations, asymptotic methods have long been used. In recent decades there has been a renaissance period of the asymptotic methods of linear mathematical physics. The range of their applicability has expanded: the asymptotic methods have been not only continuously used in traditional branches of mathematical physics but also have had an essential impact on the development of the general theory of partial differential equations. It appeared recently that there is a unified approach to a number of problems which, at first sight, looked rather unrelated.
Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov
Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-16 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Book Synopsis Asymptotic Analysis Of Differential Equations (Revised Edition) by : White Roscoe B
Download or read book Asymptotic Analysis Of Differential Equations (Revised Edition) written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Book Synopsis Asymptotic methods in mechanics of solids by : Svetlana M. Bauer
Download or read book Asymptotic methods in mechanics of solids written by Svetlana M. Bauer and published by Birkhäuser. This book was released on 2015-05-30 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic.
