  For a real-valued function V from the Faddeev-Marchenko class, we prove the
norm resolvent convergence, as \epsilon goes to 0, of a family S_\epsilon of
one-dimensional Schr\"odinger operators on the line of the form S_\epsilon:=
-D^2 + \epsilon^{-2} V(x/\epsilon). Under certain conditions the family of
potentials converges in the sense of distributions to the first derivative of
the Dirac delta-function, and then the limit of S_\epsilon might be considered
as a "physically motivated" interpretation of the one-dimensional Schr\"odinger
operator with potential \delta'.
