A method for computation of scattering amplitudes and Green functions of whole axis problems

Raúl Castillo Pérez; Vladislav V. Kravchenko; Sergii M. Torba

doi:10.1002/mma.5691

A method for computation of scattering amplitudes and Green functions of whole axis problems

Raúl Castillo Pérez, Vladislav V. Kravchenko, Sergii M. Torba

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A method for the computation of scattering data and of the Green function for the one-dimensional Schrödinger operator (Formula presented.) 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.

Original language	English
Pages (from-to)	5106-5117
Number of pages	12
Journal	Mathematical Methods in the Applied Sciences
Volume	42
Issue number	15
DOIs	https://doi.org/10.1002/mma.5691
State	Published - 1 Oct 2019

Keywords

Green's function
Neumann series of Bessel functions
Schrödinger equation
generalized eigenfunction expansion
scattering data

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title = "A method for computation of scattering amplitudes and Green functions of whole axis problems",

abstract = "A method for the computation of scattering data and of the Green function for the one-dimensional Schr{\"o}dinger operator (Formula presented.) 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.",

keywords = "Green's function, Neumann series of Bessel functions, Schr{\"o}dinger equation, generalized eigenfunction expansion, scattering data",

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T1 - A method for computation of scattering amplitudes and Green functions of whole axis problems

AU - Castillo Pérez, Raúl

AU - Kravchenko, Vladislav V.

AU - Torba, Sergii M.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - A method for the computation of scattering data and of the Green function for the one-dimensional Schrödinger operator (Formula presented.) 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.

AB - A method for the computation of scattering data and of the Green function for the one-dimensional Schrödinger operator (Formula presented.) 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.

KW - Green's function

KW - Neumann series of Bessel functions

KW - Schrödinger equation

KW - generalized eigenfunction expansion

KW - scattering data

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JF - Mathematical Methods in the Applied Sciences

IS - 15

ER -

A method for computation of scattering amplitudes and Green functions of whole axis problems

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Keywords

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