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

Abstract

An application of a quantum wave impedance method for a study of quantummechanical systems which contain 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 δ, double δ and single δ − δ ′ potentials. The formalization of solving systems with an arbitrary combination of a piesewise constant potential and a δ-potentials with the help of a quantum wave impedance approach is described.

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

“…On the base of both a periodic (Z(x+L) = Z(x)) and a matching condition for a δ-potential [24] we find that…”

“…where k is a Bloch's quasi wave-vector. For a calculation of [th(φ)] we use a matching [24] and a periodic condition Z(L − 0) = Z(0−). Consequently, we get that…”

Numerical study of quantum mechanical systems using a quantum wave impedance approach

“…In this section we are going to do this using as an example such a zero-range potential as a δ-potential. For this we use the results of papers [19,20,18,21].…”

Analytical representation of an iterative formula for a quantum wave impedance determination in a case of a piecewise constant potential

“…The other very effective method of a theoretical investigation of a quantum mechanical systems is a quantum wave impedance approach [20,21,22,23,24]. In [22] we otained the wellknown iterative formula for a quantum wave impedance determination and in [25] we discussed a numerical investigation of systems with complicated geometry of a potential using this iterative approach.…”