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Focusing on the multidimensional Schrödinger operator with a periodic potential, this book tackles both direct and inverse problems, emphasizing perturbation theory and the determination of spectral invariants. It presents a novel method for deriving asymptotic formulas for Bloch eigenvalues and functions in any dimension. The text constructs and estimates iso-energetic surfaces in high energy regions, supporting the Bethe-Sommerfeld conjecture. Additionally, it provides an algorithm for uniquely determining the potential using Bloch eigenvalues as input data.
Nákup knihy
Multidimensional Periodic Schrödinger Operator, Oktay Veliev
- Jazyk
- Rok vydania
- 2016
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- Titul
- Multidimensional Periodic Schrödinger Operator
- Podtitul
- Perturbation Theory and Applications
- Jazyk
- anglicky
- Autori
- Oktay Veliev
- Vydavateľ
- Springer International Publishing
- Rok vydania
- 2016
- Väzba
- mäkká
- Počet strán
- 252
- ISBN13
- 9783319386713
- Kategórie
- Príroda všeobecne
- Anotácia
- Focusing on the multidimensional Schrödinger operator with a periodic potential, this book tackles both direct and inverse problems, emphasizing perturbation theory and the determination of spectral invariants. It presents a novel method for deriving asymptotic formulas for Bloch eigenvalues and functions in any dimension. The text constructs and estimates iso-energetic surfaces in high energy regions, supporting the Bethe-Sommerfeld conjecture. Additionally, it provides an algorithm for uniquely determining the potential using Bloch eigenvalues as input data.