Property C for ODE and applications to inverse problems

Details Property C for ODE and applications to inverse problems Property C for ODE and applications to inverse problems

1999-11-25

arxiv.org/abs/math-ph/9911032v1

Physics

Mathematical Physics

Scientific paper

Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schr\"odinger operators. Many applications of this property to inverse problems and inverse scattering problems are given. It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.

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