124 research outputs found
Example of two different potentials which have practically the same fixed-energy phase shifts
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
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