Inverse scattering problem in a~class of nonlocal potentials.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 1, pp. 30-51
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Inverse scattering problem is formulated for the scalar Schrödinger equation on
the semi-axis in a family of phase – equivalent (nonlocal, in general case) potentials.
A new method of solving this problem is suggested which satisfies the solvability,
unambiguity and constructivity conditions. Initial assumptions of the method are essentially
based on physically general conditions of two-particle unitarity, orthogonality
and completeness of the wave functions. It is shown that in the case of scattering
data corresponding to the Riemann–Hilbert problem solvable in the class of rational
functions, the principal integral equation of the method is reduced on a dense
subclass of separable finite rank potentials to a system of algebraic second order equations.
Extension of the method to the relativistic case is carried out. A number of related
problems exactly solvable by the metod suggested is discussed.
@article{TMF_1987_70_1_a2,
author = {V. M. Muzafarov},
title = {Inverse scattering problem in a~class of nonlocal {potentials.~I}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {30--51},
publisher = {mathdoc},
volume = {70},
number = {1},
year = {1987},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1987_70_1_a2/}
}
V. M. Muzafarov. Inverse scattering problem in a~class of nonlocal potentials.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 1, pp. 30-51. http://geodesic.mathdoc.fr/item/TMF_1987_70_1_a2/