Faddeev eigenfunctions for point potentials in two dimensions

Piotr Grinevich (1) , Roman Novikov (2)

1 L.D. Landau Institute for Theoretical Physics of RAS
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Piotr Grinevich, Roman Novikov. Faddeev eigenfunctions for point potentials in two dimensions. Physics Letters A, 2012, 376, pp.1102-1106. ⟨10.1016/j.physleta.2012.02.025⟩. ⟨hal-00632264⟩