  We study the interpolation property of Sobolev spaces of order 1 denoted by
$W^{1}_{p,V}$, arising from Schr\"{o}dinger operators with positive potential.
We show that for $1\leq p_1<p<p_2<q_{0}$ with $p>s_0$, $W^{1}_{p,V}$ is a real
interpolation space between $W_{p_1,V}^{1}$ and $W_{p_2,V}^{1}$ on some classes
of manifolds and Lie groups. The constants $s_{0}, q_{0}$ depend on our
hypotheses.
