This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.

This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schr dinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.

The proceedings of the conference is devoted mainly to the mathematically rigorous approaches to the problems of quantum mechanics. The spectral properties of Schroedinger operators, including those on regions with a boundary and their generalizations, scattering theory and resonances, time-dependent Hamiltonians and quantum chaos, problems of statistical physics like spin systems, and others are discussed.

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 SchrAdinger and Dirac operators and generalized SchrAdinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications. Contributors: SchrAdinger and Dirac operators: M.Sh. Birman, V. Grecchi, R. Hempel, M. Hoffmann-Ostenhof, Y. Saito, G. Stolz, M. Znojil a Generalized SchrAdinger operators: J.-P. Antoine, J.F. Brasche, P. Duclos, R. Hempel, M. Klein, P. Stovicek a Stochastic spectral analysis: M. Demuth, V.A. Liskevich, E.M. Ouhabaz, P. Stollmann a Many-body problems and statistical physics: M. Fannes, R. Gielerak, M. HA1/4bner, A.M. Khorunzhy, H. Lange, N. Macris, Yu.A. Petrina, K.B. Sinha, A. Verbeure a Chaos: J. Dittrich, P. Seba, K. Zyczkowski a Operator theory and its application: F. Bentosela, V. Buslaev, A.N. Kochubei, A.Yu. Konstantinov, V. Koshmanenko, H. Neidhardt, G. Nenciu, D. Robert

The shared purpose in this collection of papers is to apply the theory of self-adjoint extensions of symmetry operators in various areas of physics. This allows the construction of exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields. The 20 papers selected for these proceedings give an overview of this field of research unparallelled in the published literature; in particular the views of the leading schools are clearly presented. The book will be an important source for researchers and graduate students in mathematical physics for many years to come. In these proceedings, researchers and graduate students in mathematical physics will find ways to construct exactly solvable models in quantum mechanics, quantum field theory, high energy physics, solid-state physics, microelectronics and other fields.

This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrodinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires."

Almost ?fteen years later, and there is little change in our motivation. Mathem- ical physics of quantum systems remains a lively subject of intrinsic interest with numerous applications, both actual and potential. Intheprefacetothe?rsteditionwehavedescribedtheoriginofthisbookrooted at the beginning in a course of lectures. With this fact in mind, we were naturally pleased to learn that the volume was used as a course text in many points of the world and we gladly accepted the o?er ofSpringer Verlag which inherited the rights from our original publisher, to consider preparation of a second edition. It was our ambition to bring the reader close to the places where real life dwells, and therefore this edition had to be more than a corrected printing. The ?eld is developing rapidly and since the ?rst edition various new subjects have appeared; as a couple of examples let us mention quantum computing or the major progress in theinvestigationofrandomSchr] odingeroperators.Thereare, however, goodsources intheliteraturewherethereadercanlearnabouttheseandothernewdevelopments.

Almost ?fteen years later, and there is little change in our motivation. Mathem- ical physics of quantum systems remains a lively subject of intrinsic interest with numerous applications, both actual and potential. Intheprefacetothe?rsteditionwehavedescribedtheoriginofthisbookrooted at the beginning in a course of lectures. With this fact in mind, we were naturally pleased to learn that the volume was used as a course text in many points of the world and we gladly accepted the o?er ofSpringer Verlag which inherited the rights from our original publisher, to consider preparation of a second edition. It was our ambition to bring the reader close to the places where real life dwells, and therefore this edition had to be more than a corrected printing. The ?eld is developing rapidly and since the ?rst edition various new subjects have appeared; as a couple of examples let us mention quantum computing or the major progress in theinvestigationofrandomSchr] odingeroperators.Thereare, however, goodsources intheliteraturewherethereadercanlearnabouttheseandothernewdevelopments.