The Green's function of a five-point discretization of a two-dimensional finite-gap Schrödinger operator: the case of four singular points of the spectral curve

2014/02/12 by Vasilevskiy Boris, Boris, Vasilevskiy
Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1402.2732

openalex publication_date 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a five-point discretization of a two-dimensional finite-gap for a fixed energy Schrödinger operator. We construct the Green's function of the operator. In appears as the explicit formula in terms of the integral by the specific contour on the spectral curve of the differential which is constructed by the wave function and its double. The formula is parametrized by the point on the spectral curve and for almost every parameter value it gives the Green's function with known growth at infinity.

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