  We calculate a two-pion wave function for the I=2 $S$-wave two-pion system
with a finite scattering momentum and estimate the interaction range between
two pions, which allows us to examine the validity of a necessary condition for
the finite size formula presented by Rummukainen and Gottlieb. We work in the
quenched approximation employing the plaquette gauge action for gluons and the
improved Wilson action for quarks at $1/a=1.63 {\rm GeV}$ on $32^3\times 120$
lattice. The quark masses are chosen to give $m_\pi = 0.420$, 0.488 and $0.587
{\rm GeV}$. We find that the energy dependence of the interaction range is
small and the necessary condition is satisfied for our range of the quark mass
and the scattering momentum, $k \le 0.16 {\rm GeV}$. We also find that the
scattering phase shift can be obtained with a smaller statistical error from
the two-pion wave function than from the two-pion time correlator.
