Mathematical Results in Quantum Mechanics: International Conference in Blossin (Germany), May 17–21, 1993: 70 (Operator Theory: Advances and Applications) - Tapa blanda

The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem­ porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat­ ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan­ ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts.

This book contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. Its purpose is to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book is addressed to the wide audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical problems. The reader will find sections not only on traditional subjects such as Schrodinger and Dirac operators and generalized Schrodinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications. Contributors: Schrodinger and Dirac operators: M.Sh. Birman, V. Grecchi, R. Hempel, M. Hoffmann-Ostenhof, Y. Saito, G. Stolz, M. Znojil * Generalized Schrodinger operators: J.-P. Antoine, J.F. Brasche, P. Duclos, R. Hempel, M. Klein, P. Stovicek * Stochastic spectral analysis: M. Demuth, V.A. Liskevich, E.M. Ouhabaz, P. Stollmann * Many-body problems and statistical physics: M. Fannes, R. Gielerak, M. Hubner, A.M. Khorunzhy, H. Lange, N. Macris, Yu.A. Petrina, K.B. Sinha, A. Verbeure * Chaos: J. Dittrich, P. Seba, K. Zyczkowski * Operator theory and its application: F. Bentosela, V. Buslaev, A.N. Kochubei, A.Yu. Konstantinov, V. Koshmanenko, H. Neidhardt, G. Nenciu, D. Robert