  Classically, reflectionless kinks transmit all incident radiation. Recently,
we have used an analyticity argument together with a solution of the
Lippmann-Schwinger equation to write down the leading quantum correction to the
reflection probability. The argument was fast but rather indirect. In the
present paper, we calculate the reflection coefficient and probability by
methodically grinding through the Schrodinger picture time evolution. We find
the same answer. This answer contains contributions not considered in the
traditional calculation of meson-kink scattering in 1991. However, as a result
of these contributions, our total result is zero in the case of the Sine-Gordon
model, and so is consistent with integrability.
