  We discuss an exact relation between the two-particle scattering amplitude
and the Bethe-Salpeter (BS) wave function inside the interaction range in
quantum field theory. In the relation the reduced BS wave function defined by
the BS wave function plays an essential role. Through the relation the on-shell
and half off-shell amplitudes can be calculated. We also show that the solution
of Schr\"odinger equation with the effective potential determined from the BS
wave function gives a correct on-shell scattering amplitude only at the
momentum where the effective potential is determined. Furthermore we discuss a
derivative expansion of the reduced BS wave function and a condition to obtain
results independent of the interpolating operators in the time-dependent HALQCD
method.
