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010   $a9783031490354
024 7 $a10.1007/978-3-031-49035-4
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035   $a(DE-He213)978-3-031-49035-4
035   $a(EXLCZ)9930597568800041
100   $a20240227d2024      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aMultidimensional Periodic Schrödinger Operator $ePerturbation Theories for High Energy Regions and Their Applications /$fby Oktay Veliev
205   $a3rd ed. 2024.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024.
215   $a1 online resource (420 pages)
225 1 $aSpringer Tracts in Modern Physics,$x1615-0430 ;$v291
311 08$a9783031490347 
320   $aIncludes bibliographical references and index.
327   $aPreliminary Facts -- From One-dimensional to Multidimensional -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions and Some Generalization.
330   $aThis book describes the direct and inverse problems of the multidimensional Schrödinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe?Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schrödinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schrödinger operator, periodic potentials, and other fundamental areas of mathematical physics. The book's comprehensive approach equips both students and researchers with the tools to tackle complex problems and contribute to the ongoing exploration of quantum phenomena.
410  0$aSpringer Tracts in Modern Physics,$x1615-0430 ;$v291
606   $aQuantum theory
606   $aOperator theory
606   $aDifferential equations
606   $aCondensed matter
606   $aMathematical physics
606   $aQuantum Physics
606   $aOperator Theory
606   $aDifferential Equations
606   $aCondensed Matter Physics
606   $aMathematical Physics
615  0$aQuantum theory.
615  0$aOperator theory.
615  0$aDifferential equations.
615  0$aCondensed matter.
615  0$aMathematical physics.
615 14$aQuantum Physics.
615 24$aOperator Theory.
615 24$aDifferential Equations.
615 24$aCondensed Matter Physics.
615 24$aMathematical Physics.
676   $a515.625
700   $aVeliev$b Oktay$0792319
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910842294003321
996   $aMultidimensional Periodic Schrödinger Operator$91771629
997   $aUNINA