  In this note we consider a class of $q$-hypergeometric equations describing
the quantum difference equation for the cotangent bundle over projective space
$X=T^{*}\mathbb{P}^n$ . We show that over $\mathbb{Q}_p$ these equations are
equipped with the Frobenius action $z\to z^p$. We obtain an explicit formula
for the constant term of the Frobenius intertwiner in therms of $p$-adic
$q$-gamma function of Koblitz. In the limit $q\to 1$ our formula degenerates to
the Frobenius intertwiners for the hypergeometric differential equations
discovered by B.Dwork.
