Quantum Mechanics
Volume 2

Area 02 – Scienze fisiche

The first set of papers in this volume concerns with the quantum-mechanical description of non relativistic interactions represented by nonlocal potentials. Non locality is a peculiar feature appearing in the analysis of many-body systems, e.g., in atomic physics, condensed-matter physics, and nuclear physics. At the beginning of the sixties of the past century the role which was played by nonlocal potentials could be summarized by the following sentence of Tullio Regge: “Maybe nonlocal potentials are there, but if they are there we do not know what to do with them.” Since then Viano gave valuable contributions, in particular, in the study of the mathematical aspects. 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.

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