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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Veliev, Oktay (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Springer Tracts in Modern Physics, 263
Temas:
Quantum physics.
Condensed matter.
Mathematical physics.
Quantum Physics.
Condensed Matter Physics.
Mathematical Physics.
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-319-16643-8
003 DE-He213
005 20220113004842.0
007 cr nn 008mamaa
008 150328s2015 sz | 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 
050 4 |a QC173.96-174.52 
072 7 |a PHQ  |2 bicssc 
072 7 |a SCI057000  |2 bisacsh 
072 7 |a PHQ  |2 thema 
082 0 4 |a 530.12  |2 23 
100 1 |a Veliev, Oktay.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Multidimensional Periodic Schrödinger Operator  |h [electronic resource] :  |b Perturbation Theory and Applications /  |c by Oktay Veliev. 
250 |a 1st ed. 2015. 
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 1615-0430 ;  |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 Quantum physics. 
650 0 |a Condensed matter. 
650 0 |a Mathematical physics. 
650 1 4 |a Quantum Physics. 
650 2 4 |a Condensed Matter Physics. 
650 2 4 |a Mathematical Physics. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319166445 
776 0 8 |i Printed edition:  |z 9783319166421 
776 0 8 |i Printed edition:  |z 9783319386713 
830 0 |a Springer Tracts in Modern Physics,  |x 1615-0430 ;  |v 263 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-16643-8  |z Texto Completo 
912 |a ZDB-2-PHA 
912 |a ZDB-2-SXP 
950 |a Physics and Astronomy (SpringerNature-11651) 
950 |a Physics and Astronomy (R0) (SpringerNature-43715) 

Ejemplares similares