= Solution
Replace the slowly varying interior wave by $C$ and $e^{ik|x-x'|}$ by one when both arguments lie within the range. The <integral> equation gives
$$
C=1-\frac{im}{k\hbar^2}\gamma C,\qquad
\gamma=\int_{-\infty}^{\infty}U(x)\,dx.
$$
Hence
$$
\boxed{C=t\simeq\frac1{1+im\gamma/(k\hbar^2)},\qquad r\simeq C-1.}
$$
The integrated strength has dimensions of <energy> <times> <length>. For $U=-\alpha\delta(x)$, $\gamma=-\alpha$ and this is exactly the result in part <S18/1/c>. For a regular weak potential the approximation sums the important ratio $m\gamma/(k\hbar^2)$ without requiring it to be small, which is why it remains useful beyond the naive first Born expansion at small <momentum>.
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