Quantum Waveguides

Description

Provides a comprehensive and rigorous exposition of the theory of quantum waveguides Covers a wide range of mathematical problems arising in this young but actively developing area Includes an extensive bibliography 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. Topics Mathematical Methods in Physics Ordinary Differential Equations Quantum Physics Theoretical, Mathematical and Computational Physics Operator Theory