Research on the Inverse Problem of Scattering
Abstract
Initially our principal concern was to obtain a better understanding of the fundamental ideas of inverse scattering and spectral theory, particularly in one dimension where the principal mechanism for obtaining potentials from spectral data, namely the Gelfand-Levitan, was well established. As we became more adept at solving inverse problems explicitly for certain kinds of spectral data, we were able to provide interesting examples and counter-example for conjectured theorems. Thus we were able to show that scattering data generally does not tell one whether a scattering potential is local or, if it is local, gives it uniquely without prior knowledge of the range of the potential. As is well-known, there is a dearth of scattering potentials, even for the one- dimensional and radial Schroedinger equations, for which the Schroedinger equation can be solved in terms of elementary functions. We have provided many new solvable potentials.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1981
- Accession Number
- ADA113868
Entities
People
- Harry E. Moses