Multidimensional periodic Schrödinger operator: perturbation theory and applications
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 eigenvalu...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
2019
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | zbMATH |
| Zusammenfassung: | 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 second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 326 Seiten Illustrationen |
| ISBN: | 9783030245771 |
Internformat
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| 100 | 1 | |a Veliev, Oktay |e Verfasser |0 (DE-588)1069891983 |4 aut | |
| 245 | 1 | 0 | |a Multidimensional periodic Schrödinger operator |b perturbation theory and applications |c Oktay Veliev |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cham |b Springer |c 2019 | |
| 300 | |a XII, 326 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a 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 second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow | |
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Datensatz im Suchindex
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| author | Veliev, Oktay |
| author_GND | (DE-588)1069891983 |
| author_facet | Veliev, Oktay |
| author_role | aut |
| author_sort | Veliev, Oktay |
| author_variant | o v ov |
| building | Verbundindex |
| bvnumber | BV049417725 |
| classification_rvk | UK 3000 |
| ctrlnum | (OCoLC)1410706817 (DE-599)KXP1679766570 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV049417725 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:07:04Z |
| indexdate | 2024-07-10T10:06:32Z |
| institution | BVB |
| isbn | 9783030245771 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034744704 |
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| physical | XII, 326 Seiten Illustrationen |
| publishDate | 2019 |
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| spelling | Veliev, Oktay Verfasser (DE-588)1069891983 aut Multidimensional periodic Schrödinger operator perturbation theory and applications Oktay Veliev 2. ed. Cham Springer 2019 XII, 326 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index 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 second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow Störungstheorie (DE-588)4128420-3 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Mehrdimensionalität (DE-588)4474159-5 gnd rswk-swf Bloch-Funktion (DE-588)4436775-2 gnd rswk-swf Schrödinger operator Perturbation (Mathematics) Spectral theory (Mathematics) Mehrdimensionalität (DE-588)4474159-5 s (DE-627) Hamilton-Operator (DE-588)4072278-8 s Bloch-Funktion (DE-588)4436775-2 s Störungstheorie (DE-588)4128420-3 s DE-604 9783030245788 Erscheint auch als Online-Ausgabe Veliev, Oktay Multidimensional Periodic Schrödinger Operator Second edition Cham : Springer, 2019 1 Online-Ressource (XII, 326 Seiten) 9783030245788 https://zbmath.org/?q=an%3A1419.81004 zbMATH |
| spellingShingle | Veliev, Oktay Multidimensional periodic Schrödinger operator perturbation theory and applications Störungstheorie (DE-588)4128420-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Mehrdimensionalität (DE-588)4474159-5 gnd Bloch-Funktion (DE-588)4436775-2 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4072278-8 (DE-588)4474159-5 (DE-588)4436775-2 |
| title | Multidimensional periodic Schrödinger operator perturbation theory and applications |
| title_auth | Multidimensional periodic Schrödinger operator perturbation theory and applications |
| title_exact_search | Multidimensional periodic Schrödinger operator perturbation theory and applications |
| title_exact_search_txtP | Multidimensional periodic Schrödinger operator perturbation theory and applications |
| title_full | Multidimensional periodic Schrödinger operator perturbation theory and applications Oktay Veliev |
| title_fullStr | Multidimensional periodic Schrödinger operator perturbation theory and applications Oktay Veliev |
| title_full_unstemmed | Multidimensional periodic Schrödinger operator perturbation theory and applications Oktay Veliev |
| title_short | Multidimensional periodic Schrödinger operator |
| title_sort | multidimensional periodic schrodinger operator perturbation theory and applications |
| title_sub | perturbation theory and applications |
| topic | Störungstheorie (DE-588)4128420-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Mehrdimensionalität (DE-588)4474159-5 gnd Bloch-Funktion (DE-588)4436775-2 gnd |
| topic_facet | Störungstheorie Hamilton-Operator Mehrdimensionalität Bloch-Funktion |
| url | https://zbmath.org/?q=an%3A1419.81004 |
| work_keys_str_mv | AT velievoktay multidimensionalperiodicschrodingeroperatorperturbationtheoryandapplications |