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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.
Buchkauf
Multidimensional Periodic Schrödinger Operator, Oktay Veliev
- Sprache
- Erscheinungsdatum
- 2016
- product-detail.submit-box.info.binding
- (Paperback)
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- Titel
- Multidimensional Periodic Schrödinger Operator
- Untertitel
- Perturbation Theory and Applications
- Sprache
- Englisch
- Autor*innen
- Oktay Veliev
- Erscheinungsdatum
- 2016
- Einband
- Paperback
- Seitenzahl
- 252
- ISBN13
- 9783319386713
- Kategorie
- Naturwissenschaften
- Beschreibung
- 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.