Abstract:
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.
Citation:
D. I. Abramov, “Reconstruction of the interaction potential in quasiclassical scattering”, TMF, 58:2 (1984), 244–253; Theoret. and Math. Phys., 58:2 (1984), 160–166
\Bibitem{Abr84}
\by D.~I.~Abramov
\paper Reconstruction of the interaction potential in quasiclassical scattering
\jour TMF
\yr 1984
\vol 58
\issue 2
\pages 244--253
\mathnet{http://mi.mathnet.ru/tmf4331}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=743410}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 58
\issue 2
\pages 160--166
\crossref{https://doi.org/10.1007/BF01017922}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984TG27600010}
Linking options:
https://www.mathnet.ru/eng/tmf4331
https://www.mathnet.ru/eng/tmf/v58/i2/p244
This publication is cited in the following 5 articles:
B V Budyak, B N Zakhariev, “New exactly solvable models for the Schrodinger equation”, Inverse Problems, 3:1 (1987), 125
M. N. Popushoi, “On the inverse problem for the scattering theory of charged particles when there is a linear relationship between the energy, the square of the orbital angular momentum, and the Coulomb coupling constant”, Theoret. and Math. Phys., 69:3 (1986), 1272–1278
I. V. Poplavskii, “Generalized Darboux–Crum–Krein transformations”, Theoret. and Math. Phys., 69:3 (1986), 1278–1282
D. I. Abramov, “Equations of the quantum inverse scattering method in the semiclassical limit”, Theoret. and Math. Phys., 63:1 (1985), 344–356
I. V. Bogdanov, “Inverse problem of mechanics in momentum space”, Soviet Physics Journal, 28:1 (1985), 40
Citation in format AMSBIB
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