Article
Example of two different potentials which have practically the same fixed-energy phase shifts
Physics Letters A
(1999)
Abstract
The Newton-Sabatier procedure for finding the potential from fixed-energy phase shifts is analyzed. A method is proposed for finding two quite different spherically-symmetric real-valued, piecewise-constant, compactly supported potentials which generate at a fixed energy the phase shifts δℓ which are practically indistinguishable for all ℓ. In particular, an explicit concrete example of two such potentials qj, j = 1,2 is demonstrated. These potentials have the properties: (1) sup |q11 − q2| > 3, and qj, j = 1,2, are of order of magnitude 1, (2) δl(1) = δl(2) for l = 0, …,4 and |δl(1) − δl(2)| ≤ 10−5, l > 4.
Disciplines
Publication Date
April 12, 1999
DOI
https://doi.org/10.1016/S0375-9601(99)00134-6
Publisher Statement
Elsevier
Citation Information
Ruben G. Hayrapetyan, Alexander G. Ramm and Alexandra B. Smirnova. "Example of two different potentials which have practically the same fixed-energy phase shifts" Physics Letters A Vol. 254 Iss. 3 (1999) p. 141 - 148 ISSN: 0375-9601 Available at: http://works.bepress.com/ruben-hayrapetyan/53/