DTIC ADA113868: Research on the Inverse Problem pdf

DTIC ADA113868: Research on the Inverse Problem

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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

• Creator/s: Defense Technical Information Center
• Date: 10/1/1981
• Year: 1981
• Book Topics/Themes: DTIC Archive, Moses, Harry E., LOWELL UNIV MA CENTER FOR ATMOSPHERIC RESEARCH, *TRANSMISSION LINES, *INVERSE SCATTERING, *ACOUSTIC FIELDS, SCATTERING CROSS SECTIONS, RESONANCE SCATTERING, EMISSION SPECTRA, HYDROGEN, LINEAR FILTERING, OPERATORS(MATHEMATICS), SCHRODINGER EQUATION, VARIATIONAL PRINCIPLES, ATOMIC SPECTRA, POTENTIAL THEORY

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