Scattering Theory: Some Old and New Problems

• Basic concepts.- Short-range interactions. asymptotic completeness.- Short-range interactions. Miscellaneous.- Long-range interactions. The scheme of smooth perturbations.- The generalized fourier transform.- Long-range matrix potentials.- A stationary representation.- The short-range case.- The long-range case.- The relative scattering matrix.- Setting the scattering problem.- Resolvent equations for three-particle systems.- Asymptotic completeness. A sketch of proof.- The scattering matrix and eigenfunctions for multiparticle systems.- New channels of scattering.- The heisenberg model.- Infinite obstacle scattering.

“This book provides a modern survey of important problems of the mathematical scattering theory. … The book fills a gap in the literature because it emphasizes the stationary approach to the scattering theory problems.” (Michael Perelmuter, zbMATH 0951.35003, 2022)