Geodesic
Integral representation of the classical $S$ matrix and construction of new uniform approximations
Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 3, pp. 364-374

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An integral representation of classical $S$-matrix for one-dimensional non-linear non-stationary problem is rigorously deduced, which is valid for all values of quantum numbers, including small ones. Comparison of the quasi classical results with the exact ones for the model of oscillator with the external forces, makes it possible to estimate the error of the method of classical $S$-matrix and its uniform Eiry approximation. Possibilities of constructing new “uniform” approximations, which could be useful in many-dimensional problems of atomic collisions, are discussed. 
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     author = {M. Ya. Ovchinnikova},
     title = {Integral representation of the classical $S$ matrix and construction of new uniform approximations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {364--374},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_22_3_a8/}
}
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M. Ya. Ovchinnikova. Integral representation of the classical $S$ matrix and construction of new uniform approximations. Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 3, pp. 364-374. http://geodesic.mathdoc.fr/item/TMF_1975_22_3_a8/