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

TL;DR

This paper develops formulas and equations to derive scattering data from the Dirichlet-to-Neumann map for the Schrödinger equation with a nonzero background potential, extending previous zero-background results.

Contribution

It introduces new methods for extracting scattering data in the presence of a nonzero background potential, generalizing earlier zero-background formulas.

Findings

Formulas for scattering data with nonzero background potential

Extension of previous zero-background results

Applicable to bounded domain potentials

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