Application of a quantum wave impedance method for zero-range singular potentials

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 $\delta -{\delta }^{\mathrm{\prime }}$ 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.