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

arXiv:cond-mat/0409751 · doi:10.1088/0266-5611/21/1/016

Abstract

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 -Δψ+(v(x)-Eu(x))ψ=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)].

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