On the determination of potentials without bound state data
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We investigate the feasibility of recovering a compactly supported potential from the S-matrix. For general potentials this is known to be insufficient, information on the bound states being essential. We prove uniqueness results and derive reconstruction algorithms for potential recovery, using several different combinations of S-matrix data. The basic device is the transformation of the scattering data into boundary conditions for a related hyperbolic boundary value problem. Some generalizations to the case of step-like potentials are proved. © 1994.
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