Quantum Scattering Theory for Several Particle Systems (Mathematical Physics and Applied Mathematics)

Faddeev, L.D.; Merkuriev, S.P.

ISBN 10: 9048143055 / ISBN 13: 9789048143054

Edité par Springer, 2010

In. N° de réf. du vendeur ria9789048143054_new

Synopsis :

The last decade witnessed an increasing interest of mathematicians in prob- lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es- pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif- ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem- mas and theorems is not appropriate for the contemporary writing on mathe- matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe- matical statements. Of special importance are the results and methods that have been developed in this way for the first time.

Présentation de l'éditeur: This volume is devoted to the quantum mechanical problem of the scattering of N -particles. This has long been a traditional and difficult problem of mathematical physics and its quantum analogue has many interesting applications in atomic and nuclear physics. It is also an interesting problem from a mathematical point of view. The book has seven chapters. Chapter 1 deals with the basic dynamical concepts, and wave and scattering operators are defined and their general properties are described. Chapter 2 considers the stationary formalism of scattering theory. The method of integral equations is the subject of Chapter 3. Chapters 4 and 5 are devoted to the study of wave equations in configuration space. Chapter 6 covers some problems in the mathematical foundation of scattering theory, and the final chapter discusses a number of applications of stationary scattering theory. The book concludes with comments on the existing literature and a bibliography. For researchers in mathematics and mathematical physics interested in quantum mechanical scattering theory.

Détails bibliographiques

Titre : Quantum Scattering Theory for Several ...
Éditeur : Springer
Date d'édition : 2010
Reliure : Couverture souple
Etat : New