  We observe that the ratio of the on-shell scattering amplitude to the
Bethe-Salpeter (BS) wave function outside the interaction range is almost
independent of time in our quenched calculation of the $I=2$ two-pion
scattering with almost zero momentum. In order to discuss the time
independence, we present a relation between the two-pion scattering amplitude
and the surface term of the BS wave function at the boundary. Using the
relation under some assumptions, we show that the ratio is independent of time
if the two-pion four-point function in early time is dominated by scattering
states with almost zero momentum in addition to the ground state of the
two-pion scattering.
