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Inverse and Algebraic Quantum Scattering Theory

Inverse and Algebraic Quantum Scattering Theory PDF Author: Barnabas Apagyi
Publisher: Springer
ISBN: 3662141450
Category : Science
Languages : en
Pages : 402

Book Description
This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.

Inverse and Algebraic Quantum Scattering Theory

Inverse and Algebraic Quantum Scattering Theory PDF Author: Barnabas Apagyi
Publisher: Springer
ISBN: 3662141450
Category : Science
Languages : en
Pages : 402

Book Description
This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.

Quantum Inverse Scattering Method and Correlation Functions

Quantum Inverse Scattering Method and Correlation Functions PDF Author: V. E. Korepin
Publisher: Cambridge University Press
ISBN: 9780521586467
Category : Mathematics
Languages : en
Pages : 582

Book Description
The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

The Inverse Problem of Scattering Theory

The Inverse Problem of Scattering Theory PDF Author: Z.S. Agranovich
Publisher: Courier Dover Publications
ISBN: 0486842495
Category : Mathematics
Languages : en
Pages : 307

Book Description
This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.

Operator Theory and Its Applications

Operator Theory and Its Applications PDF Author: Alexander G. Ramm
Publisher: American Mathematical Soc.
ISBN: 0821819909
Category : Mathematics
Languages : en
Pages : 594

Book Description
Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.

Quantum Inversion Theory and Applications

Quantum Inversion Theory and Applications PDF Author: H.V.v. Geramb
Publisher: Springer
ISBN: 3662139693
Category : Science
Languages : en
Pages : 491

Book Description
This volume covers aspects of Schr|dinger equation inversion for the purposeof determining interaction potentials in particle, nuclear and atomic physics from experimental data. It includes reviews and reports on the latest developments in mathematics, supersymmetric quantum mechanics, inversion for fixed-l nucleon-nucleon potentials, inversion of fixed-E optical potentials and their generalizations. Also included are some topics on nonlinear differential equations relating to theSchr|dinger or other equations of particle, nuclear, atomic and molecular physics which can be solved by inverse scattering transformations. The material collected in this volume gives a clear picture of the status ofresearch in this rapidly growing field. The book addresses students and young scientists as well as researchers in theoretical physics and functional analysis.

Inverse Problems in Quantum Scattering Theory

Inverse Problems in Quantum Scattering Theory PDF Author: Khosrow Chadan
Publisher: Springer Science & Business Media
ISBN: 3642833179
Category : Science
Languages : en
Pages : 526

Book Description
The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.

An Introduction to Inverse Scattering and Inverse Spectral Problems

An Introduction to Inverse Scattering and Inverse Spectral Problems PDF Author: Khosrow Chadan
Publisher: SIAM
ISBN: 0898713870
Category : Mathematics
Languages : en
Pages : 206

Book Description
Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Theory of Solitons

Theory of Solitons PDF Author: S. Novikov
Publisher: Springer Science & Business Media
ISBN: 9780306109775
Category : Mathematics
Languages : en
Pages : 298

Book Description


An Introduction To Inverse Problems In Physics

An Introduction To Inverse Problems In Physics PDF Author: Mohsen Razavy
Publisher: World Scientific
ISBN: 9811221685
Category : Science
Languages : en
Pages : 387

Book Description
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.

Continuous Optimization

Continuous Optimization PDF Author: V. Jeyakumar
Publisher: Springer Science & Business Media
ISBN: 0387267719
Category : Mathematics
Languages : en
Pages : 454

Book Description
Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.