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Non-self-adjoint schrödinger operator with a periodic potentialspectral theories for scalar and vectorial cases and their generalizations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Non-self-adjoint schrödinger operator with a periodic potentialby Oktay Veliev.
Reminder of title:	spectral theories for scalar and vectorial cases and their generalizations /
Author:	Veliev, Oktay.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xv, 472 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Schrödinger operator.
Online resource:	https://doi.org/10.1007/978-3-031-90259-8
ISBN:	9783031902598$q(electronic bk.)

Non-self-adjoint schrödinger operator with a periodic potentialspectral theories for scalar and vectorial cases and their generalizations /
Veliev, Oktay.

Non-self-adjoint schrödinger operator with a periodic potentialspectral theories for scalar and vectorial cases and their generalizations /[electronic resource] :by Oktay Veliev. - Second edition. - Cham :Springer Nature Switzerland :2025. - xv, 472 p. :ill. (chiefly color), digital ;24 cm.

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.

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.

ISBN: 9783031902598$q(electronic bk.)

Standard No.: 10.1007/978-3-031-90259-8doiSubjects--Topical Terms:

980099
Schrödinger operator.

LC Class. No.: QC174.17.S3

Dewey Class. No.: 530.124

Non-self-adjoint schrödinger operator with a periodic potentialspectral theories for scalar and vectorial cases and their generalizations /
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505 0 $a 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.
520 $a 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.
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