Asymptotic Methods In Quantum Mechanics
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Asymptotic Methods In Quantum Mechanics
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Author : S.H. Patil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Methods In Quantum Mechanics written by S.H. Patil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Asymptotic Theory Of Quantum Statistical Inference Selected Papers
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Author : Masahito Hayashi
language : en
Publisher: World Scientific
Release Date : 2005-02-21
Asymptotic Theory Of Quantum Statistical Inference Selected Papers written by Masahito Hayashi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-21 with Science categories.
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Semi Classical Approximation In Quantum Mechanics
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Author : Victor P. Maslov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Semi Classical Approximation In Quantum Mechanics written by Victor P. Maslov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Science categories.
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.
Asymptotic Methods In Quantum Mechanics
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Author : S H Patil
language : en
Publisher:
Release Date : 2000-04-26
Asymptotic Methods In Quantum Mechanics written by S H Patil and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-26 with categories.
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.
Short Wavelength Diffraction Theory
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Author : Vasili M. Babic
language : en
Publisher: Springer
Release Date : 2011-12-08
Short Wavelength Diffraction Theory written by Vasili M. Babic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Science categories.
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.
Asymptotic Methods For Integrals
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Author : Nico M. Temme
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015
Asymptotic Methods For Integrals written by Nico M. Temme and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differential equations categories.
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.
Asymptotic Methods For Engineers
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Author : Igor V. Andrianov
language : en
Publisher: CRC Press
Release Date : 2024-05-20
Asymptotic Methods For Engineers written by Igor V. Andrianov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-20 with Mathematics categories.
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.).
Asymptotic Methods In The Theory Of Plates With Mixed Boundary Conditions
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Author : Igor Andrianov
language : en
Publisher: John Wiley & Sons
Release Date : 2014-02-06
Asymptotic Methods In The Theory Of Plates With Mixed Boundary Conditions written by Igor Andrianov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-06 with Science categories.
Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.
Introduction To Quantum Mechanics Schrodinger Equation And Path Integral Second Edition
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Author : Harald J W Muller-kirsten
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-07-19
Introduction To Quantum Mechanics Schrodinger Equation And Path Integral Second Edition written by Harald J W Muller-kirsten and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-19 with Science categories.
This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Advanced Mathematical Methods For Scientists And Engineers I
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Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.