Difference Schrödinger equation and quasisymmetric polynomials
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We study the singularity of solutions of the Schrödinger equation with a finite potential at the point k = 0. In the case of delta-type potentials, we show that the nature of this singularity is automodel in a certain sense. We discuss using the obtained results to construct an approximate solution of the inverse scattering problem on the whole axis. For this, we introduce the concept of a quasisymmetric polynomial associated with a given curve.
KeywordsSchrödinger operator Green’s function additional spectrum difference model
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- 5.U. V. Barkina and S. N. Melikhov, Vladikavkaz. Mat. Zh., 16, No. 4, 27–40 (2014).Google Scholar