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Focusing on the multidimensional Schrödinger operator with a periodic potential, this book delves into both direct and inverse problems essential for perturbation theory and spectral analysis. It offers thorough derivations of asymptotic formulas for Bloch eigenvalues and functions, while also addressing iso-energetic surfaces in high-energy contexts. A significant contribution is the validation of the Bethe-Sommerfeld conjecture across dimensions and lattices. The updated edition adds a chapter on lower-dimensional cases, enhancing the foundational understanding for subsequent higher-dimensional discussions.
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Multidimensional Periodic Schrödinger Operator, Oktay Veliev
- Language
- Released
- 2020
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- (Paperback)
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- Title
- Multidimensional Periodic Schrödinger Operator
- Subtitle
- Perturbation Theory and Applications
- Language
- English
- Authors
- Oktay Veliev
- Publisher
- Springer International Publishing
- Released
- 2020
- Format
- Paperback
- Pages
- 340
- ISBN13
- 9783030245801
- Category
- Nature in general
- Description
- Focusing on the multidimensional Schrödinger operator with a periodic potential, this book delves into both direct and inverse problems essential for perturbation theory and spectral analysis. It offers thorough derivations of asymptotic formulas for Bloch eigenvalues and functions, while also addressing iso-energetic surfaces in high-energy contexts. A significant contribution is the validation of the Bethe-Sommerfeld conjecture across dimensions and lattices. The updated edition adds a chapter on lower-dimensional cases, enhancing the foundational understanding for subsequent higher-dimensional discussions.