Comments on the letter of P.Sabatier "An erroneous statement"
Ramm, A. G.
arXiv, 0308025 / Harvested from arXiv
In his letter Sabatier writes that my statement {\bf "The Newton-Sabatier (NS) method for inverting the fixed-energy phase shifts for a potential is fundamentally wrong"} is erroneous. In [2] my statement is proved. It is explained in [2] that the foundations of the NS method are wrong, and, in particular, that the basic integral equation of this method, in general is not uniquely solvable for some $r>0$, contrary to the implicit assumption of the NS method. If this equation is not uniquely solvable for some $r>0$, then the NS method breaks down: it produces a potential which is not locally integrable. Consequently, my conclusion was: {\it the NS theory as an inverse scattering theory is fundamentally wrong in the sense that its foundations are wrong}. This conclusion is fully justified in [2]. Additional comments on the Sabatier's letter are given.
Publié le : 2003-08-21
Classification:  Mathematical Physics,  34R30, 81U05, 81U40
@article{0308025,
     author = {Ramm, A. G.},
     title = {Comments on the letter of P.Sabatier "An erroneous statement"},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0308025}
}
Ramm, A. G. Comments on the letter of P.Sabatier "An erroneous statement". arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0308025/