Application of a quantum wave impedance method for study of infinite and semi-infinite periodic media

This paper is dedicated to an application of a quantum wave impedance approach for a study of infinite and semi-infinite periodic systems. Both a Dirac comb and a $\delta -{\delta }^{\mathrm{\prime }}$ comb as well as a Kronig-Penney model are considered. It was shown how to reformulate the problem of an investigation of mentioned systems in terms of a quantum wave impedance and it was demonstrated how much a quantum wave impedance approach simplifies studying these systems compared to other methods. The illustation of such a simplification was provided by application of classical approach, transfer matrix technique and a quatum wave impedance method for solving Kronig-Penney model.