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000726373 020__ $$a9783319166438$$qelectronic book
000726373 020__ $$a3319166433$$qelectronic book
000726373 020__ $$z9783319166421
000726373 0247_ $$a10.1007/978-3-319-16643-8$$2doi
000726373 035__ $$aSP(OCoLC)ocn906152737
000726373 035__ $$aSP(OCoLC)906152737
000726373 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dUPM$$dCOO$$dYDXCP$$dOCLCF
000726373 049__ $$aISEA
000726373 050_4 $$aQC174.17.S3
000726373 08204 $$a530.12/4$$223
000726373 1001_ $$aVeliev, Oktay,$$eauthor.
000726373 24510 $$aMultidimensional periodic Schrödinger operator$$h[electronic resource] :$$bperturbation theory and applications /$$cOktay Veliev.
000726373 264_1 $$aCham :$$bSpringer,$$c2015.
000726373 300__ $$a1 online resource (x, 242 pages).
000726373 336__ $$atext$$btxt$$2rdacontent
000726373 337__ $$acomputer$$bc$$2rdamedia
000726373 338__ $$aonline resource$$bcr$$2rdacarrier
000726373 4901_ $$aSpringer tracts in modern physics,$$x0081-3869 ;$$vvolume 263
000726373 504__ $$aIncludes bibliographical references and index.
000726373 5050_ $$aPreface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions.
000726373 506__ $$aAccess limited to authorized users.
000726373 520__ $$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.
000726373 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 3, 2015).
000726373 650_0 $$aSchrödinger operator.
000726373 650_0 $$aPerturbation (Mathematics)
000726373 650_0 $$aSpectral theory (Mathematics)
000726373 77608 $$iPrint version:$$z9783319166421
000726373 830_0 $$aSpringer tracts in modern physics ;$$vvolume 263.
000726373 852__ $$bebk
000726373 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-16643-8$$zOnline Access$$91397441.1
000726373 909CO $$ooai:library.usi.edu:726373$$pGLOBAL_SET
000726373 980__ $$aEBOOK
000726373 980__ $$aBIB
000726373 982__ $$aEbook
000726373 983__ $$aOnline
000726373 994__ $$a92$$bISE