{"product_id":"9783031902581","title":"Non-Self-Adjoint Schrödinger Operator with a Periodic Potential: Spectral Theories for Scalar and Vectorial Cases and Their Generalizations","description":"\u003ch1\u003eNon-Self-Adjoint Schrödinger Operator with a Periodic Potential: Spectral Theories for Scalar and Vectorial Cases and Their Generalizations\u003c\/h1\u003e \u003ch2\u003eVeliev, Oktay\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp class=\"MsoNormal\" style=\"margin-bottom: .0001pt; line-height: normal; mso-layout-grid-align: none; text-autospace: none;\"\u003e\u003cspan lang=\"EN-GB\" style=\"mso-ansi-language: EN-GB;\"\u003eThis 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.\u003c\/span\u003e\u003c\/p\u003e\n\u003cp class=\"MsoListParagraph\" style=\"margin-bottom: .0001pt; mso-add-space: auto; line-height: normal; mso-layout-grid-align: none; text-autospace: none;\"\u003e\u003cspan lang=\"EN-GB\" style=\"mso-ansi-language: EN-GB;\"\u003eThe 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.\u003c\/span\u003e\u003c\/p\u003e\n\u003cp class=\"MsoListParagraph\" style=\"margin-bottom: .0001pt; mso-add-space: auto; line-height: normal; mso-layout-grid-align: none; text-autospace: none;\"\u003e\u003cspan lang=\"EN-GB\" style=\"mso-ansi-language: EN-GB;\"\u003eThe 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.\u003c\/span\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2025-07-03\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031902581\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-90259-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 472\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":44334662811788,"sku":"9783031902581","price":161.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031902581.jpg?v=1779653925","url":"https:\/\/lateknightbooks.com\/products\/9783031902581","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}