  In this paper we investigate the well-posedness of the Cauchy problem for a
Schr\"odinger operator with singular lower order terms. We allow distributional
coefficients and we approach this problem via the regularising methods at the
core of the theory of very weak solutions. We prove that a very weak solution
exists and it is unique modulo negligible perturbations. Very weak solutions
converge to classical solutions when the equation coefficients are regular
enough.
