Comments on the letter of P.Sabatier "An erroneous statement"
| dc.creator | Ramm, A. G. | |
| dc.date | 2003-08-21 | |
| dc.date.accessioned | 2026-07-07T04:30:28Z | |
| dc.date.available | 2026-07-07T04:30:28Z | |
| dc.description | 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. | |
| dc.description | 5pp | |
| dc.identifier | https://arxiv.org/abs/math-ph/0308025 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0308025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57476 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34R30, 81U05, 81U40 | |
| dc.title | Comments on the letter of P.Sabatier "An erroneous statement" | |
| dc.type | text |