  We give explicit necessary and sufficient conditions for the boundedness of
the general second order differential operator L with real- or complex-valued
distributional coefficients acting from the Sobolev space W^{1,2}(R^n) to its
dual W^{-1,2}(R^n). This enables us to obtain analytic criteria for the
fundamental notions of relative form boundedness, compactness, and
infinitesimal form boundedness of L with respect to the Laplacian on L^2(R^n).
  In particular, we establish a complete characterization of the form
boundedness of the Schroedinger operator (i \nabla + a)^2 + q with magnetic
vector potential a \in L^2_{loc} and q \in D'(\R^n).
