Abstract:
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.
Fulltext:
PDF file (481 kB)