An algorithm for finding the periodic potential of the three-dimensional Schrodinger operator from spectral invariants
AuthorVeliev, Oktay A.
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CitationVELİEV, O.A. (2011). An algorithm for finding the periodic potential of the three-dimensional Schrodinger operator from spectral invariants. Journal of Physics A: Mathematical and Theoretical, 44 (15), 23p. http://dx.doi.org/10.1088/1751-8113/44/15/155202.
In this paper, we investigate the three-dimensional Schrodinger operator with a periodic, relative to a lattice Omega of R(3), 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 is an element of 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 is an element of V.