Volume II - Quantum Mechanics

This volume concerns with the quantum-mechanical description of non-relativistic interactions represented by nonlocal potentials. Born series convergence, scattering solutions, Levinson's theorem, phase-shifts asymptotics and eigenfunction expansions associated with SchrÖdinger operators are some of the mathematical-physics problems studied by Viano in connection with nonlocal potentials. His work culminated in the last paper on this subject, where the rigorous mathematical analysis of a class of nonlocal interactions within the framework of complex angular momentum theory was given. The second set of papers regards the study of the semi-classical limit of quantum mechanics and related problems of asymptotic analysis. The rigorous proof of the existence of diffracted rays along with the detailed mathematical study of evanescent rays and complex rays have led to the development of a "Generalized Geometrical Optics", which has found application in various problems of optics, atomic and molecular physics.