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

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The scattering problem is solved for a wave equation on the axis $(-\infty,\infty)$ with nonnegative potential $q$, $q(x)=0$, $x0$. 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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     author = {B. S. Pavlov},
     title = {On the one-dimensional scattering of plane waves on an arbitrary potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {105--115},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a11/}
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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/