Geodesic
On the one-dimensional scattering of plane waves on an arbitrary potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 105-115 Cet article a éte moissonné depuis la source Math-Net.Ru

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The scattering problem is solved for a wave equation on the axis $(-\infty,\infty)$ with nonnegative potential $q$, $q(x)=0$, $x<0$. It is shown that the, in general, nonunitary reflection coefficient is equal to the diagonal element of the complete (unitary) $S$ matrix. 
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     title = {On the one-dimensional scattering of plane waves on an arbitrary potential},
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B. S. Pavlov. On the one-dimensional scattering of plane waves on an arbitrary potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 105-115. http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a11/

[1] P. P. Kulish, Matem. zametki, 4 (1968), 677 | MR | Zbl

[2] T. Regge, Nuovo Cim., 8 (1958), 671 | DOI | MR | Zbl

[3] B. S. Pavlov, DAN SSSR, 193 (1970), 36 | MR | Zbl

[4] B. S. Pavlov, DAN SSSR, 206 (1972), 6 | MR

[5] P. Laks, R. Filipps, Teoriya rasseyaniya, «Mir», 1971 | MR

[6] E. Ch. Titchmarsh, Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. 1, IL, 1960 | MR

[7] L. D. Faddeev, UMN, 14:4 (1959), 57 | MR | Zbl

[8] K. Gofman, Banakhovy prostranstva analiticheskikh funktsii, IL, 1963

[9] M. Sh. Birman, Izv. AN SSSR, ser. matem., 27:4 (1963), 883 | MR | Zbl