Reconstruction of a Radially Symmetric Potential from Two Spectral Sequences

We consider the problem of determining a radially symmetric potential in the three-dimensional Schr¨odinger equation from eigenvalues associated with two different angular-momentum quantum numbers.This leads to a singular eigenvalue problem for which there are no known general uniqueness results for the most reasonable conjectures.W e are able to give strong evidence for uniqueness in some cases and we discuss a computational solution method together with some supporting analysis.One application we have in mind is the determination of certain physical parameters in the standard model of the sun constructed from eigenvalue data.