A method for computation of scattering amplitudes and Green functions of whole axis problems. (23rd May 2019)

• Record Type: Journal Article
• Authors: Castillo Pérez, Raúl; Kravchenko, Vladislav V.; Torba, Sergii M.
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 5106
• Page End: 5117
• Publication Date: 2019-05-23
• Subjects: generalized eigenfunction expansion -- Green's function -- Neumann series of Bessel functions -- scattering data -- Schrödinger equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5691
• Languages: English
• ISSNs: 0170-4214

Abstract

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 .