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

Abstract

The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise constant function is also reasonable in a case of using a quantum impedance approach.The dependence of an accuracy of numerical calculations on a number of cascads by which a real potential is represented was found. The method of including into a consideration of zero-range singular potentials was developed.

Effective technique of numerical investigation of systems with complicated geometry of a potential

“…In the article [18] it was mentioned that in real nanosystems where the potential has a complicated geometry (spatial structure) the issue of an effective approximate calculation of parameters of such systems is not easy. Of course one can approximate a real potential by a piecewise constant potential and use the results of the [19,20,18].…”

“…In the article [18] it was mentioned that in real nanosystems where the potential has a complicated geometry (spatial structure) the issue of an effective approximate calculation of parameters of such systems is not easy. Of course one can approximate a real potential by a piecewise constant potential and use the results of the [19,20,18]. But as it was shown in [18] to obtain the satisfactory accuracy one has to use a lot of breaking points of a real potential which in turn means a significant increasing of necessary computational operations.…”

“…Of course one can approximate a real potential by a piecewise constant potential and use the results of the [19,20,18]. But as it was shown in [18] to obtain the satisfactory accuracy one has to use a lot of breaking points of a real potential which in turn means a significant increasing of necessary computational operations.…”

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.…”

Finite periodic $δ-δ'$ comb

“…In our previous papers [19,20,21,22,23,24,25,26] we demonstarted how a quantum wave impedance method can be applied to the investigation of infinite and semi-infinite periodic structures which contain both a piesewise constant potential and zero-range singular potentials, namely δ and δ − δ while in [27] we developed an approach to a study of systems with a complicated geometry of a potential. Next step we have done in [28], where a technique of theoretical study of finit periodic structures using the advantures of both transfer matrix approach and a quantum wave impedance method was proposed.…”