Theoretical and Mathematical Physics

, Volume 184, Issue 2, pp 1067–1077 | Cite as

Difference Schrödinger equation and quasisymmetric polynomials

  • A. B. Shabat


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.


Schrödinger operator Green’s function additional spectrum difference model 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASMoscowRussia

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