Delta models of oscillatory structures and passband filters

2020

Preprint

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.

Section: Discussionmentioning

confidence: 99%

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

2020

Preprint

“…Obtained results are directly related to a design of nanodevices with the desired characteristics since they allows relating the characteristics of a device with the structure of its potential. An additional argument in favor of use a quantum wave impedance method is that it demands ferew calculations compared to the transfer matrix approach and in many papers [10,11,26,27,28,29,30] it was demonstrated its efficacy for an analysis of quantum-mechanical structures with a potential which has a complicated spatial structure.…”

Section: Discussionmentioning

confidence: 99%

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

2020

Preprint

An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for a transmission probability as a function of a particle energy for an arbitrary cascad of constant potentials was obtained. The application of obtained results was illustrated on a system of doublewell/barrier structures.

“…Although this approach is quite good and allows transiting the relations obtained within a transmission line theory to quantum mechanical systems it is still worth to get the relations for a quantum mechanical impedance from the first principles because it will open the other dimensions of a quantum wave impedance method. But nor in the paper [6] nor in the further papers (see for example [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]) dedicated to a quantum wave impedance, the systematic introduction of this concept and consistent theory based on the first principles were not proposed. The aim of this article is to fill this gap by constructing such a theory starting from the Srödinger equation; to demonstrate an application of a quantum wave impedance for solving both scattering and bound states problems.…”

Section: Introductionmentioning

confidence: 99%

Reformulation of a transmission and reflection problems in terms of a quantum wave impedance function

2020

Preprint

On the base of a 1D Shrödinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a single rectangular barrier. Both the scattering and the bound states problem were reformulated in terms of a quantum wave impedance and its application for solving both these problems was considered. The expressions for a reflection and a transmission coefficient were found on the base of a quantum wave impedance approach.