The generic-potential bounded-eigenfunction problem on flat manifolds

Let $(M,g)$ be a flat manifold and let $\Delta_g+V$ be a Schrödinger operator on $(M,g)$. Generic-potential bounded-eigenfunction problem. For generic $V$, are the eigenfunctions uniformly bounded? The source presents this as a converse-direction problem and notes that multiplicities create difficulties; no resolution is given.