Example of two different potentials which have practically the same fixed-energy phase shifts
摘要
It is shown that the Newton-Sabatier procedure for inverting the fixed-energy phase shifts for a potential is not an inversion method but a parameter-fitting procedure. Theoretically there is no guarantee that this procedure is applicable to the given set of the phase shifts, if it is applicable, there is no guaran- tee that the potential it produces generates the phase shifts from which it was reconstructed. Moreover, no generic potential, specifically, no potential which is not analytic in a neighborhood of the positive real semiaxis can be reconstructed by the Newton-Sabatier procedure. A numerical method is given for finding spherically symmetric compactly supported potentials which produce practically the same set of fixed-energy phase shifts for all values of angular momentum. Concrete example of such potentials is given.
引用
@article{arxiv.math-ph/9911037,
title = {Example of two different potentials which have practically the same fixed-energy phase shifts},
author = {R. Airapetyan and A. G. Ramm and A. Smirnova},
journal= {arXiv preprint arXiv:math-ph/9911037},
year = {2009}
}