Title Multidimensional Periodic Schr??dinger Operator : Perturbation Theory and Applications Author(s) Veliev, Oktay Publication Cham, Springer International Publishing, 2015. Description X, 242 p : online resource Abstract Note The book describes the direct problems and the inverse problem of the multidimensional Schr??dinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given ISBN,Price 9783319166438 Keyword(s) 1. EBOOK 2. EBOOK - SPRINGER 3. MATHEMATICAL PHYSICS 4. QUANTUM PHYSICS 5. SOLID STATE PHYSICS Item Type eBook Multi-Media Links Please Click here for eBook Circulation Data Accession#   Call# Status Issued To Return Due On Physical Location I07212     On Shelf