TY - JOUR
T1 - Example of two different potentials which have practically the same fixed-energy phase shifts
AU - Hayrapetyan, Ruben G.
AU - Ramm, Alexander G.
AU - Smirnova, Alexandra B.
N1 - 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 δ ℓ which are practically indistinguishable for all ℓ.
PY - 1999/4/12
Y1 - 1999/4/12
N2 - 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.
AB - 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.
UR - https://www.sciencedirect.com/science/article/abs/pii/S0375960199001346?via%3Dihub
U2 - 10.1016/S0375-9601(99)00134-6
DO - 10.1016/S0375-9601(99)00134-6
M3 - Article
VL - 254
JO - Physics Letters A
JF - Physics Letters A
ER -