  An application of a quantum wave impedance method for a study of
quantum-mechanical systems which con\-tain singular zero-range potentials is
considered. It was shown how to reformulate the problem of an investigation of
mentioned systems in terms of a quantum wave impedance. As a result both the
scattering and bound states problems are solved for systems of single $\delta$,
double $\delta$ and single $\delta-\delta'$ potentials. The formalization of
solving systems with an arbitrary combination of a piesewise constant potential
and a $\delta$-potentials with the help of a quantum wave impedance approach is
described.
