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In this note we consider the parabolic Anderson model in one dimension withtime-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 findthe quenched asymptotics for the solution we consider its Feynman-Kacrepresentation and explore the asymptotics of the principal eigenvalue for arandom operator of the form $\frac{1}{2} \Delta + \dot{W}$.

Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise