Comments on the letter of P.Sabatier "An erroneous statement"

Abstract

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.