  We study the operator $L=-\Delta+q$ on a bounded domain $\Omega\subset\mathbb
R^n$, where $q(x)$ is a distributional potential. We find sufficient conditions
for $q(x)$ which guarantee that $L$ is well--defined with Dirichlet and
generalized Neumann boundary conditions. The asymptotics of the eigenvalues and
the basis properties of the eigen- and associated functions of such operators
are studied. The results are generalized for strongly elliptic operator of
order $2m$ with Dirichlet boundary conditions.
