Classical limit of the quantum inverse scattering problem

The passage to the limit of classical mechanics is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number $l>0$ in the lowest order of perturbation theory. It is shown how in the limit $l>0$ in the quantum inverse problem the integral Abel transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation.