Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Multidimensional Periodic Schrödinger Operator: Perturbation Theories for High Energy Regions and Their Applications

Multidimensional Periodic Schrödinger Operator: Perturbation Theories for High Energy Regions and Their Applications

Veliev, Oktay

Hardcover

Series: Springer Tracts in Modern Physics, Book 291

General MathematicsPhysics

ISBN10: 3031490347
ISBN13: 9783031490347
Publisher: Springer
Published: Feb 29 2024
Pages: 411
Weight: 1.70
Height: 0.94 Width: 6.14 Depth: 9.21
Language: English
This book describes the direct and inverse problems of the multidimensional Schrödinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential.

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