LEADER 04464nam 22006255 450 001 9911015865203321 005 20250703130248.0 010 $a9783031902598$b(electronic bk.) 010 $z9783031902581 024 7 $a10.1007/978-3-031-90259-8 035 $a(MiAaPQ)EBC32196002 035 $a(Au-PeEL)EBL32196002 035 $a(CKB)39578311500041 035 $a(DE-He213)978-3-031-90259-8 035 $a(OCoLC)1527724696 035 $a(EXLCZ)9939578311500041 100 $a20250703d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNon-Self-Adjoint Schrödinger Operator with a Periodic Potential $eSpectral Theories for Scalar and Vectorial Cases and Their Generalizations /$fby Oktay Veliev 205 $a2nd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (777 pages) 311 08$aPrint version: Veliev, Oktay Non-Self-Adjoint Schrödinger Operator with a Periodic Potential Cham : Springer International Publishing AG,c2025 9783031902581 327 $a1.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. 330 $aThis 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. 606 $aMathematical physics 606 $aQuantum theory 606 $aCondensed matter 606 $aOptics 606 $aTheoretical, Mathematical and Computational Physics 606 $aQuantum Physics 606 $aMathematical Methods in Physics 606 $aCondensed Matter Physics 606 $aOptics and Photonics 615 0$aMathematical physics. 615 0$aQuantum theory. 615 0$aCondensed matter. 615 0$aOptics. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aQuantum Physics. 615 24$aMathematical Methods in Physics. 615 24$aCondensed Matter Physics. 615 24$aOptics and Photonics. 676 $a530.1 700 $aVeliev$b Oktay$0792319 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911015865203321 996 $aNon-Self-adjoint Schrödinger Operator with a Periodic Potential$92569164 997 $aUNINA