Example of two different potentials which have practically the same fixed-energy phase shifts

Details Example of two different potentials which have practically the same fixed-energy phase shifts Example of two different potentials which have practically the same fixed-energy phase shifts

1999-11-26

arxiv.org/abs/math-ph/9911037v1

Phys LettA254,N3-4, (1999), 141-148

Physics

Mathematical Physics

Scientific paper

10.1016/S0375-9601(99)00134-6

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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