Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

Roman Novikov (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)].

Mots clés: Dirichlet-to-Neumann map; scattering data; inverse problems

Domaines: Autre [cond-mat.other]; Equations aux dérivées partielles [math.AP]

Roman Novikov. Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. Inverse Problems, 2005, 21, pp.257-270. ⟨hal-00002977⟩