Faddeev eigenfunctions for point potentials in two dimensions

TL;DR

This paper derives explicit formulas for Faddeev eigenfunctions associated with point potentials in two dimensions, including the first examples exhibiting contour singularities in the spectral parameter at fixed energy.

Contribution

It provides the first explicit formulas for Faddeev eigenfunctions with contour singularities for two-dimensional point potentials.

Findings

Explicit formulas for Faddeev eigenfunctions are obtained.

First examples with contour singularity in spectral parameter are presented.

Abstract

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.