Shabat, A. B. Discretization of the Schrödinger spectral problem. (English) Zbl 1087.39020 Inverse Probl. 18, No. 4, 1003-1011 (2002). Summary: Exact discretization of the Schrödinger operator in connection with one-dimensional inverse scattering theory and the Riemann-Hilbert problem are discussed. By comparing the discrete and the continuous Green functions, qualitative estimates for the discrete spectral problem are obtained. Birational automorphisms of transparent potentials are described. MSC: 39A12 Discrete version of topics in analysis 39A70 Difference operators 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 34A55 Inverse problems involving ordinary differential equations 34L25 Scattering theory, inverse scattering involving ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain PDFBibTeX XMLCite \textit{A. B. Shabat}, Inverse Probl. 18, No. 4, 1003--1011 (2002; Zbl 1087.39020) Full Text: DOI