Multidimensional Periodic Schrödinger Operator Perturbation Theory and Applications /

The 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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Veliev, Oktay (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
Σειρά:Springer Tracts in Modern Physics, 263
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 02931nam a22004815i 4500
001 978-3-319-16643-8
003 DE-He213
005 20151204184201.0
007 cr nn 008mamaa
008 150328s2015 gw | s |||| 0|eng d
020 |a 9783319166438  |9 978-3-319-16643-8 
024 7 |a 10.1007/978-3-319-16643-8  |2 doi 
040 |d GrThAP 
050 4 |a QC173.96-174.52 
072 7 |a PHQ  |2 bicssc 
072 7 |a SCI057000  |2 bisacsh 
082 0 4 |a 530.12  |2 23 
100 1 |a Veliev, Oktay.  |e author. 
245 1 0 |a Multidimensional Periodic Schrödinger Operator  |h [electronic resource] :  |b Perturbation Theory and Applications /  |c by Oktay Veliev. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2015. 
300 |a X, 242 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Springer Tracts in Modern Physics,  |x 0081-3869 ;  |v 263 
505 0 |a Preface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions. 
520 |a The 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. 
650 0 |a Physics. 
650 0 |a Mathematical physics. 
650 0 |a Quantum physics. 
650 0 |a Solid state physics. 
650 1 4 |a Physics. 
650 2 4 |a Quantum Physics. 
650 2 4 |a Solid State Physics. 
650 2 4 |a Mathematical Physics. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783319166421 
830 0 |a Springer Tracts in Modern Physics,  |x 0081-3869 ;  |v 263 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-16643-8  |z Full Text via HEAL-Link 
912 |a ZDB-2-PHA 
950 |a Physics and Astronomy (Springer-11651)