This book describes the direct and inverse problems of the multidimensional Schrödinger 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.
| ISBN: | 9783031490378 |
| Publication date: | 2nd April 2025 |
| Author: | Oktay Veliev |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 411 pages |
| Series: | Springer Tracts in Modern Physics |
| Genres: |
Quantum physics (quantum mechanics and quantum field theory) Functional analysis and transforms Differential calculus and equations Condensed matter physics (liquid state and solid state physics) Mathematical physics |
This book describes the direct and inverse problems of the multidimensional Schrödinger 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.
Multidimensional Periodic Schrödinger Operator features in the following genres: Quantum physics (quantum mechanics and quantum field theory), Functional analysis and transforms, Differential calculus and equations, Condensed matter physics (liquid state and solid state physics), Mathematical physics
Paperback, Hardback. £107.99, down from the £119.99 cover price. Not Available.
Multidimensional Periodic Schrödinger Operator was written by Oktay Veliev and published by Springer an imprint of Springer International Publishing
Multidimensional Periodic Schrödinger Operator has 411 pages
Yes it is part of Springer Tracts in Modern Physics series
£107.99, reduced from £119.99. Not Available.