Multidimensional Periodic Schrödinger Operator Perturbation Theories for High Energy Regions and Their 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...
-д хадгалсан:
| Үндсэн зохиолч: | |
|---|---|
| Байгууллагын зохиогч: | |
| Формат: | Цахим Цахим ном |
| Хэл сонгох: | англи |
| Хэвлэсэн: |
Cham :
Springer International Publishing : Imprint: Springer,
2024.
|
| Хэвлэл: | 3rd ed. 2024. |
| Цуврал: | Springer Tracts in Modern Physics,
291 |
| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.1007/978-3-031-49035-4 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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MARC
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| 100 | 1 | |a Veliev, Oktay. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Multidimensional Periodic Schrödinger Operator |h [electronic resource] : |b Perturbation Theories for High Energy Regions and Their Applications / |c by Oktay Veliev. |
| 250 | |a 3rd ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (XIII, 411 p. 1 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Use of colour is Not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
| 341 | 0 | |b Next / Previous structural navigation |2 onix | |
| 341 | 0 | |b All Non-decorative content supports reading without sight |2 onix | |
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Tracts in Modern Physics, |x 1615-0430 ; |v 291 | |
| 505 | 0 | |a Preliminary Facts -- From One-dimensional to Multidimensional -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions and Some Generalization. | |
| 520 | |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 and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schrödinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schrödinger operator, periodic potentials, and other fundamental areas of mathematical physics. The book's comprehensive approach equips both students and researchers with the tools to tackle complex problems and contribute to the ongoing exploration of quantum phenomena. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Quantum physics. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Condensed matter. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Quantum Physics. |
| 650 | 2 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Condensed Matter Physics. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031490347 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031490361 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031490378 |
| 830 | 0 | |a Springer Tracts in Modern Physics, |x 1615-0430 ; |v 291 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-49035-4 |
| 912 | |a ZDB-2-PHA | ||
| 912 | |a ZDB-2-SXP | ||
| 950 | |a Physics and Astronomy (SpringerNature-11651) | ||
| 950 | |a Physics and Astronomy (R0) (SpringerNature-43715) | ||