An algorithm for finding the periodic potential of the three-dimensional Schrödinger operator from spectral invariants
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Publication:2999475
DOI10.1088/1751-8113/44/15/155202zbMATH Open1213.81211arXiv0903.1402OpenAlexW2007108463MaRDI QIDQ2999475
Author name not available (Why is that?)
Publication date: 13 May 2011
Published in: (Search for Journal in Brave)
Abstract: In this paper, we investigate the three-dimensional Schrodinger operator with a periodic, relative to a lattice {Omega} of R3, potential q. A special class V of the periodic potentials is constructed, which is easily and constructively determined from the spectral invariants. First, we give an algorithm for the unique determination of the potential q in V of the three-dimensional Schrodinger operator from the spectral invariants that were determined constructively from the given Bloch eigenvalues. Then we consider the stability of the algorithm with respect to the spectral invariants and Bloch eigenvalues. Finally, we prove that there are no other periodic potentials in the set of large class of functions whose Bloch eigenvalues coincides with the Bloch eigenvalues of q in V.
Full work available at URL: https://arxiv.org/abs/0903.1402
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