Phase-Integral Method

Phase-Integral Method
Author: Nanny Fröman
Publisher: Springer Science & Business Media
Total Pages: 258
Release: 2013-04-09
Genre: Mathematics
ISBN: 1461223423

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.

Physical Problems Solved by the Phase-Integral Method

Physical Problems Solved by the Phase-Integral Method
Author: Nanny Fröman
Publisher: Cambridge University Press
Total Pages: 230
Release: 2002-06-13
Genre: Science
ISBN: 1139434322

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
Total Pages: 178
Release: 2013-06-03
Genre: Mathematics
ISBN: 0486316297

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.

An Introduction to Phase-Integral Methods

An Introduction to Phase-Integral Methods
Author: John Heading
Publisher: Courier Corporation
Total Pages: 178
Release: 2013-01-01
Genre: Mathematics
ISBN: 0486497429

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.

Stark Effect In A Hydrogenic Atom Or Ion: Treated By The Phase-integral Method With Adjoined Papers By A Hokback And P O Froman

Stark Effect In A Hydrogenic Atom Or Ion: Treated By The Phase-integral Method With Adjoined Papers By A Hokback And P O Froman
Author: Nanny Froman
Publisher: World Scientific
Total Pages: 162
Release: 2008-03-14
Genre: Science
ISBN: 1908979062

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

Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application

Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Author: S. G. Ahmed
Publisher: Bentham Science Publishers
Total Pages: 647
Release: 2022-06-30
Genre: Mathematics
ISBN: 9815040898

The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

Two-Phase Flow

Two-Phase Flow
Author: Cl Kleinstreuer
Publisher: Routledge
Total Pages: 472
Release: 2017-11-01
Genre: Science
ISBN: 1351406485

This graduate text provides a unified treatment of the fundamental principles of two-phase flow and shows how to apply the principles to a variety of homogeneous mixture as well as separated liquid-liquid, gas-solid, liquid-solid, and gas-liquid flow problems, which may be steady or transient, laminar or turbulent.Each chapter contains several sample problems, which illustrate the outlined theory and provide approaches to find simplified analytic descriptions of complex two-phase flow phenomena.This well-balanced introductory text will be suitable for advanced seniors and graduate students in mechanical, chemical, biomedical, nuclear, environmental and aerospace engineering, as well as in applied mathematics and the physical sciences. It will be a valuable reference for practicing engineers and scientists. A solutions manual is available to qualified instructors.

Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals
Author: Norman Bleistein
Publisher: Courier Corporation
Total Pages: 453
Release: 1986-01-01
Genre: Mathematics
ISBN: 0486650820

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.

Quantum Optics in Phase Space

Quantum Optics in Phase Space
Author: Wolfgang P. Schleich
Publisher: John Wiley & Sons
Total Pages: 717
Release: 2011-02-16
Genre: Science
ISBN: 3527635009

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
Total Pages: 743
Release: 2013-12-01
Genre: Mathematics
ISBN: 9400903650

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.