  In this note we consider the parabolic Anderson model in one dimension with
time-independent fractional noise $\dot{W}$ in space. We consider the case
$H<\frac{1}{2}$ and get existence and uniqueness of solution. In order to find
the quenched asymptotics for the solution we consider its Feynman-Kac
representation and explore the asymptotics of the principal eigenvalue for a
random operator of the form $\frac{1}{2} \Delta + \dot{W}$.
