An application of a quantum wave impedance method to finite periodic structures

TL;DR

This paper introduces a quantum wave impedance method applied to finite periodic structures, combining transfer matrix and impedance approaches for analyzing complex nanosystems with localized potentials.

Contribution

It establishes a connection between quantum wave impedance and transfer/scattering matrices, enabling improved analysis of nanosystems with complex potentials.

Findings

Derived expressions for Tamm's levels in Dirac comb systems.

Unified transfer matrix and impedance methods for quantum systems.

Demonstrated applicability to complex nanoscale structures.

Abstract

The relations between a quantum wave impedance function and elements of transfer and scattering matrixes for quantum mechanical systems with arbitrary localized form of potential were established. Obtained results allows using the advantages of both methods, namely a transfer matrix technique and a quantum wave impedance approach, for an investigating of nanosystems with a complicated geometry of a potential. A finit Dirac comb was solved and expressions for Tamm's levels in this system were derived within both approaches.