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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik Non-Self-Adjoint Schrödinger Operator with a Periodic Potential
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Non-Self-Adjoint Schrödinger Operator with a Periodic Potential
Oktay Veliev (Gebundene Ausgabe, Englisch)
★★★★★
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.07.2025
Sprache
Englisch
EAN
9783031902581
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Oktay Veliev
Seitenanzahl
472
Auflage
2
Einbandart
Gebundene Ausgabe
Buch Untertitel
Spectral Theories for Scalar and Vectorial Cases and Their Generalizations
Schlagwörter
Non-self-adjoint Operators, Schrödinger Operators, Periodic Differential Operators, PT-Symmetric Quantum Mechanics, Periodic Optical Potential, Spectral Analysis of the Schrödinger Operator, Mathieu-Hill Operator, Spectral Expansion of the Hill Operator, Matheiu-Schrödinger Operator, Non-Self-Adjoint Spectral Theory, Schrödinger Operator with Periodic Potential, Periodic Sturm-Liouville Operators, Advanced Spectral Theory Applications, Complex-Valued Optical Potentials, Quantum Mechanics Spectral Classification
Thema-Inhalt
PHU - Mathematische Physik
PHQ - Quantenphysik (Quantenmechanik und Quantenfeldtheorie)
PHFC - Physik der kondensierten Materie (Flüssigkeits- und Festkörperphysik)
PHJ - Optische Physik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Palgrave Macmillan, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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