| 书目名称 | Multidimensional Periodic Schrödinger Operator |
| 副标题 | Perturbation Theorie |
| 编辑 | Oktay Veliev |
| 视频video | |
| 概述 | Features a now complete theory of self-adjoint Schrödinger operators within periodic potentials valid in all dimensions.Opens up new horizons for spectral analysis of quantum mechanical operators.Repr |
| 丛书名称 | Springer Tracts in Modern Physics |
| 图书封面 |  |
| 描述 | 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..This updated and significantly expanded third edition features an extension of this framework |
| 出版日期 | Book 2024Latest edition |
| 关键词 | Bloch Eigenvalues; Derivatives of Band Functions; Inverse Problem of Multidimensional; Isoenergetic Sur |
| 版次 | 3 |
| doi | https://doi.org/10.1007/978-3-031-49035-4 |
| isbn_softcover | 978-3-031-49037-8 |
| isbn_ebook | 978-3-031-49035-4Series ISSN 0081-3869 Series E-ISSN 1615-0430 |
| issn_series | 0081-3869 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 17:24:43
