Multidimensional Periodic Schrodinger Operator : Perturbation Theories for High Energy Regions and Their Applications EPUB
by Oktay Veliev
Part of the Springer Tracts in Modern Physics series
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This book describes the direct and inverse problems of the multidimensional Schrodinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential.
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- Format:EPUB
- Publisher:Springer International Publishing
- Publication Date:27/02/2024
- Category:
- ISBN:9783031490354
Information
-
Download Now
- Format:EPUB
- Publisher:Springer International Publishing
- Publication Date:27/02/2024
- Category:
- ISBN:9783031490354