Geodesic
Classical limit of the quantum inverse scattering problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 35-43

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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. 
@article{TMF_1985_65_1_a3,
     author = {I. V. Bogdanov},
     title = {Classical limit of the quantum inverse scattering problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {35--43},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a3/}
}
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I. V. Bogdanov. Classical limit of the quantum inverse scattering problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 35-43. http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a3/