  The dynamic reflection probability and the spectral reflection probability
for a one-dimensional Schroedinger operator $H = - \Delta + V$ are
characterized in terms of the scattering theory of the pair $(H, H_\infty)$
where $H_\infty$ is the operator obtained by decoupling the left and right
half-lines $\mathbb{R}_{\leq 0}$ and $\mathbb{R}_{\geq 0}$. An immediate
consequence is that these reflection probabilities are in fact the same, thus
providing a short and transparent proof of the main result of Breuer, J., E.
Ryckman, and B. Simon (2010) . This approach is inspired by recent developments
in non-equilibrium statistical mechanics of the electronic black box model and
follows a strategy parallel to the Jacobi case.
