Reconstruction of the interaction potential in quasiclassical scattering
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 244-253
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The reconstruction of a local spherically symmetric potential from
scattering data is considered in the quasiclassical approximation
for the case when the scattering data are known on some curve in
the energy-angular momentum plane. In this plane a twoparameter
family of curves is found for which the problem reduces to an Abel
integral equation, and solutions are obtained that generalize the
known solutions for constant energy and for constant angular
momentum. It is shown that the solution of the quasiclassical
inverse scattering problem is a combination of the solutions of
two independent classical problems with different initial data –
the scattering angle and the delay time. Cases are described in
which the result can be represented in the form of an explicit
function.
@article{TMF_1984_58_2_a9,
author = {D. I. Abramov},
title = {Reconstruction of the interaction potential in quasiclassical scattering},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {244--253},
publisher = {mathdoc},
volume = {58},
number = {2},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a9/}
}
D. I. Abramov. Reconstruction of the interaction potential in quasiclassical scattering. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 244-253. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a9/