2022-01-26T06:58:27Zhttps://openaccess.dogus.edu.tr/oai/requestoai:openaccess.dogus.edu.tr:11376/25502020-09-22T18:32:29Zcom_11376_129com_11376_101com_11376_3388col_11376_2551
Veliev, Oktay A.
2016-05-12T12:07:41Z
2016-05-12T12:07:41Z
2015
Veliev, O. A. (2015). Multidimensional periodic Schrödinger operator: Perturbation theory and applications. New York, Springer.
9783319166421
978-3319166438
0081-3869
1615-0430
https://dx.doi.org/10.1007/978-3-319-16643-8
https://hdl.handle.net/11376/2550
263
The book describes the direct problems and the inverse problem of the multidimensional Schrödinger 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.
eng
info:eu-repo/semantics/restrictedAccess
Quantum Physics
Solid State Physics
Mathematical Physics
Multidimensional periodic Schrödinger operator: Perturbation theory and applications
book