Non-Self-Adjoint Schrödinger Operator with a Periodic Potential : Spectral Theories for Scalar and Vectorial Cases and Their Generalizations / / by Oktay Veliev
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| Autore: |
Veliev Oktay
|
| Titolo: |
Non-Self-Adjoint Schrödinger Operator with a Periodic Potential : Spectral Theories for Scalar and Vectorial Cases and Their Generalizations / / by Oktay Veliev
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
| Edizione: | 2nd ed. 2025. |
| Descrizione fisica: | 1 online resource (777 pages) |
| Disciplina: | 530.1 |
| Soggetto topico: | Mathematical physics |
| Quantum theory | |
| Condensed matter | |
| Optics | |
| Theoretical, Mathematical and Computational Physics | |
| Quantum Physics | |
| Mathematical Methods in Physics | |
| Condensed Matter Physics | |
| Optics and Photonics | |
| Nota di contenuto: | 1.Introduction and Overview -- 2.Spectral Theory for the Schr¨odinger Operator with a ComplexValued Periodic Potential -- 3.On the Special Potentials -- 4.On the Mathieu-Schr¨odinger Operator -- 5.PT-Symmetric Periodic Optical Potential -- 6.On the Schr¨odinger Operator with a Periodic Matrix Potential -- 7.Some Generalizations and Supplements. |
| Sommario/riassunto: | This book offers a comprehensive exploration of spectral theory for non-self-adjoint differential operators with complex-valued periodic coefficients, addressing one of the most challenging problems in mathematical physics and quantum mechanics: constructing spectral expansions in the absence of a general spectral theorem. It examines scalar and vector Schrödinger operators, including those with PT-symmetric periodic optical potentials, and extends these methodologies to higher-order operators with periodic matrix coefficients. The second edition significantly expands upon the first by introducing two new chapters that provide a complete description of the spectral theory of non-self-adjoint differential operators with periodic coefficients. The first of these new chapters focuses on the vector case, offering a detailed analysis of the spectral theory of non-self-adjoint Schrödinger operators with periodic matrix potentials. It thoroughly examines eigenvalues, eigenfunctions, and spectral expansions for systems of one-dimensional Schrödinger operators. The second chapter develops a comprehensive spectral theory for all ordinary differential operators, including higher-order and vector cases, with periodic coefficients. It also includes a complete classification of the spectrum for PT-symmetric periodic differential operators, making this edition the most comprehensive treatment of these topics to date. The book begins with foundational topics, including spectral theory for Schrödinger operators with complex-valued periodic potentials, and systematically advances to specialized cases such as the Mathieu–Schrödinger operator and PT-symmetric periodic systems. By progressively increasing the complexity, it provides a unified and accessible framework for students and researchers. The approaches developed here open new horizons for spectral analysis, particularly in the context of optics, quantum mechanics, and mathematical physics. |
| Titolo autorizzato: | Non-Self-adjoint Schrödinger Operator with a Periodic Potential |
| ISBN: | 9783031902598 |
| 9783031902581 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9911015865203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |