Geodesic
$S$-matrix problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 2, pp. 169-180 
V. A. Kolkunov. $S$-matrix problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a1/
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     author = {V. A. Kolkunov},
     title = {$S$-matrix problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {2},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the approximate solution of the one-dimensional Schrödinger equation, obtained by replacing the potential by a step function, leads to the study of a multiplicative integral, for the analysis of which a graphical method is developed. A parametrization of the $S$-matrix in terms of Euler angles is used in a study of the transmission of waves through a force field, and a relation is established between the solution of the equation and Lobachevskii geometry.

[1] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatgiz, 1958 | Zbl

[2] S. N. Sokolov, Preprint R-906, OIYaI, 1963 | MR

[3] F. R. Gantmakher, Teoriya matrits, «Nauka», 1967 | MR