P. G. Grinevich, R. G. Novikov, “Faddeev eigenfunctions for moltipoint potentials”, Eurasian Journal of Mathematical and Computer Applications, 2013, Volume 1, Issue 2,Pages <nobr>76

Faddeev eigenfunctions for moltipoint potentials

P. G. Grinevich^a, R. G. Novikov^b

^a CNRS — Laboratoire de Mathématiques Jean Leray, Département de Mathématiques, Universite de Nantes
^b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We present explicit formulae for the Faddeev eigenfunctions and related generalized scattering data for multipoint potentials in two and three dimensions. For single point potentials in 3D such formulae were obtained in an old unpublished work of L.D. Faddeev. For single point potentials in 2D such formulae were given recently in [11].

Keywords: Schrodinger operator, Faddeev eigenfunctions, exact solutions, point scatterers.

MSC: 81Q05, 81U15, 35C05, 47A40

Received: 01.04.2013

Language: English