Multidimensional Periodic Schrödinger Operator

Perturbation Theory and Applications

Oktay Veliev (Autor)

Buch | Softcover

X, 242 Seiten

2016 | 1. Softcover reprint of the original 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-38671-3 (ISBN)

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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.

Preface.- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions.- Constructive Determination of the Spectral Invariants.- Periodic Potential from the Spectral Invariants.- Conclusions.

Erscheinungsdatum	14.10.2016
Reihe/Serie	Springer Tracts in Modern Physics
Zusatzinfo	X, 242 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Naturwissenschaften ► Chemie ► Analytische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Bloch Eigenvalues • Derivatives of Band Functions • Inverse Problem of Multidimensional • Isoenergetic Surfaces • Mathematical Physics • Periodic Bloch Functions • Physics • Physics and Astronomy • Quantum Physics • Quantum physics (quantum mechanics and quantum fie • Schrödinger operator • Solid state physics • Spectral Invariants • Spectrum analysis, spectrochemistry, mass spectrom
ISBN-10	3-319-38671-9 / 3319386719
ISBN-13	978-3-319-38671-3 / 9783319386713
Zustand	Neuware