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101 0 $aeng
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181   $ctxt
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200 10$aMultidimensional Periodic Schrödinger Operator $ePerturbation Theory and Applications /$fby Oktay Veliev
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (X, 242 p.) 
225 1 $aSpringer Tracts in Modern Physics,$x0081-3869 ;$v263
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-16642-5 
320   $aIncludes bibliographical references and index.
327   $aPreface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions.
330   $aThe book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.
410  0$aSpringer Tracts in Modern Physics,$x0081-3869 ;$v263
606   $aQuantum theory
606   $aSolid state physics
606   $aMathematical physics
606   $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080
606   $aSolid State Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25013
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
615  0$aQuantum theory.
615  0$aSolid state physics.
615  0$aMathematical physics.
615 14$aQuantum Physics.
615 24$aSolid State Physics.
615 24$aMathematical Physics.
676   $a515.724
700   $aVeliev$b Oktay$4aut$4http://id.loc.gov/vocabulary/relators/aut$0792319
801  0$bMiAaPQ
801  1$bMiAaPQ
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906   $aBOOK
912   $a9910300423203321
996   $aMultidimensional Periodic Schrödinger Operator$91771629
997   $aUNINA