Inverse problem for complex ’’ra-analytic’’ potentials of finite range

Abstract

We present a simple solution to the inverse problem for the Schrödinger equation at fixed energy for complex ’’ra-analytic’’ potentials of finite range. This is done via an interpolation formula for the regular radial solutions as functions of complex angular momentum. The interpolation formula is derived by Frobenius techniques and Cauchy’s theorem. As an application we study an inverse problem for a spherically symmetric cold plasma perturbed by a small oscillatory electric potential of fixed (finite) frequency.