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Difference Schrödinger equation and quasisymmetric polynomials. (English. Russian original) Zbl 1329.81176
Theor. Math. Phys. 184, No. 2, 1067-1077 (2015); translation from Teor. Mat. Fiz. 184, No. 2, 200–211 (2015).
Summary: 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.

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
39A12 Discrete version of topics in analysis
35J08 Green’s functions for elliptic equations
Full Text: DOI
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