On the constructive determination of the periodic potentials from the bloch eigenvalues
CitationVeliev, O.A. (2009). On the constructive determination of the periodic potentials from the bloch eigenvalues. Journal of Physics A: Mathematical and Theoretical, 42(37) 19p. http://dx.doi.org/10.1088/1751-8113/42/37/375201
In this paper, we consider the three-dimensional Schrödinger operator with a periodic, relative to a lattice Ω of , potential q. We construct a set D of trigonometric polynomials such that D is dense in , where s > 3, in the -topology, any element q of the set D can be determined constructively and uniquely, modulo inversion and translation q(x) → q(-x), q(x) → q(x + τ), where , from the given Bloch eigenvalues of the Schrödinger operator with the potential q.