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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 200–211, August, 2015.
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Shabat, A.B. Difference Schrödinger equation and quasisymmetric polynomials. Theor Math Phys 184, 1067–1077 (2015). https://doi.org/10.1007/s11232-015-0318-7
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DOI: https://doi.org/10.1007/s11232-015-0318-7