Faddeev eigenfunctions for multipoint potentials

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 multipoint potentials in two and three dimensions. For single point potentials in 3D such formulas were obtained in an old unpublished work of L.D. Faddeev. For single point potentials in 2D such formulas were given recently in [P.G. Grinevich, R.G. Novikov, Physics Letters A,376,(2012),1102-1106].

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

Piotr Grinevich, Roman Novikov. Faddeev eigenfunctions for multipoint potentials. Eurasian Journal of Mathematical and Computer Applications, 2013, 1 (2), pp.76-91. ⟨hal-00747888⟩