  Let Lf(x)=-\Delta f(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a
non-negative self-adjoint Schr\"odinger operator on R^d. We say that an
L^1-function f belongs to the Hardy space H^1_L if the maximal function M_L
f(x)=\sup_{t>0} |e^{-tL} f(x)| belongs to L^1(R^d). We prove that under certain
assumptions on V the space H^1_L is also characterized by the Riesz transforms
R_j=\frac{\partial}{\partial x_j} L^{-1/2}, j=1,...,d, associated with L. As an
example of such a potential V one can take any V\geq 0, V\in L^1_{loc}, in one
dimension.
