  We calculate the 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. It allows us to examine the validity of the necessary condition for
the finite-volume method for the scattering phase shift. A calculation is
carried out with a plaquette gauge action for gluons and a clover-improved
Wilson action for quarks at $1/a=1.63 {\rm GeV}$ on $32^3\times 120$ lattice in
the quenched approximation. We conclude that the necessary condition is
satisfied within statistical errors for the lattice size $L\ge 32$, when the
quark mass is in the range $m_\pi^2=0.176 - 0.345 {\rm GeV}^2$ and the
scattering momentum in $k^2 < 0.026 {\rm GeV}^2$. We also find that the energy
dependence of the interaction range is small and it takes $1.2-1.7 {\rm fm}$
for our simulation parameters. We obtain the phase shift from the two-pion wave
function with a smaller statistical error than that from the conventional
analysis with the two-pion time correlator.
