Multidimensional Periodic Schrödinger Operator: Perturbation Theory and Applications
The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The...
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| Ngôn ngữ: | English |
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Springer
2016
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59786 |
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oai:scholar.dlu.edu.vn:DLU123456789-597862023-11-11T06:51:53Z Multidimensional Periodic Schrödinger Operator: Perturbation Theory and Applications Veliev, Oktay Spectral theory Perturbation Schrödinger operator The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given. 2016-03-09T07:28:35Z 2016-03-09T07:28:35Z 2015 Book 978-3-319-16643-8 978-3-319-16642-1 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59786 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Spectral theory Perturbation Schrödinger operator |
| spellingShingle |
Spectral theory Perturbation Schrödinger operator Veliev, Oktay Multidimensional Periodic Schrödinger Operator: Perturbation Theory and Applications |
| description |
The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given. |
| format |
Book |
| author |
Veliev, Oktay |
| author_facet |
Veliev, Oktay |
| author_sort |
Veliev, Oktay |
| title |
Multidimensional Periodic Schrödinger Operator:
Perturbation Theory and Applications |
| title_short |
Multidimensional Periodic Schrödinger Operator:
Perturbation Theory and Applications |
| title_full |
Multidimensional Periodic Schrödinger Operator:
Perturbation Theory and Applications |
| title_fullStr |
Multidimensional Periodic Schrödinger Operator:
Perturbation Theory and Applications |
| title_full_unstemmed |
Multidimensional Periodic Schrödinger Operator:
Perturbation Theory and Applications |
| title_sort |
multidimensional periodic schrödinger operator:
perturbation theory and applications |
| publisher |
Springer |
| publishDate |
2016 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/59786 |
| _version_ |
1782537155068821504 |