**Abstract:** We consider 1D Schroedinger operator of the form $-(d^2/d^2x) + \epsilon^{-2} Q(x/\epsilon)$. Potentials of such form approximate as $\epsilon\to 0$ the first derivative of the Dirac delta function in the topology of distributions, which served as a motivation of our study. We show that the limit operators depend on Q in a nontrivial way.