Faddeev eigenfunctions for point potentials in two dimensions

We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for point (delta-type) potentials in two dimensions. In particular, we obtain the first explicit examples of such eigenfunctions with contour singularity in spectral parameter at a fixed real energy....

Full description

Saved in:
Bibliographic Details
Published in:Physics letters. A 2012-02, Vol.376 (12-13), p.1102-1106
Main Authors: Grinevich, P.G., Novikov, R.G.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Explicitly solvable models
Faddeev eigenfunctions
Mathematical Physics
Mathematics
Monochromatic inverse scattering
Physics
Spectral singularities
Two-dimensional Schrödinger equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for point (delta-type) potentials in two dimensions. In particular, we obtain the first explicit examples of such eigenfunctions with contour singularity in spectral parameter at a fixed real energy. ► Explicit formulas for Faddeevʼs eigenfunctions for point potentials in 2D are given. ► Explicit model with contour spectral singularities at fixed real energy is found. ► The ∂¯-formulas of fixed real energies in 2D are illustrated for point potentials.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2012.02.025