A method for computation of scattering amplitudes and Green functions of whole axis problems. (23rd May 2019) - Castillo Pérez, Raúl; Kravchenko, Vladislav V.; Torba, Sergii M.
Abstract : A method for the computation of scattering data and of the Green function for the one‐dimensional Schrödinger operator H : = − d 2 d x 2 + q ( x ) with a decaying potential is presented. It is based on representations for the Jost solutions in the case of a compactly supported potential obtained in terms of Neumann series of Bessel functions (NSBF). The representations are used for calculating a complete orthonormal system of generalized eigenfunctions of the operator H, which in turn allow one to compute the scattering amplitudes and the Green function of the operator H − λ with λ ∈ C .