The energy levels and wave functions of single-electron states in nano sized quantum rings

Authors

  • Tumayev E.N. Kuban State University, Krasnodar, Российская Федерация

UDC

530.145

Abstract

The electronic states of nanoscale quantum rings containing one electron are studied. Compiled by the Schrodinger equation in the two-dimensional space, for a electron system in the ekhternal potentialfield, describing nanoscale quantum ring heterolayer semiconductor structure. As a potential describing quantum ring are considered potential Volcano and Hill. For the Hill potential theexact solutions of the two-dimensional Schrödinger equation, the study of which is usually carried out by numerical methods, are obtained. A model potential (potential of the "6-2"), describes a unified way as a quantum ring, and a quantum dot in the presence of an external homogeneous constant magnetic field. Analytical methods to obtain new exact solutions of the Schrödinger equation in the class of Heun's functions for the potential "6-2" and the capacity of the Hill. It is shown that the solution of the Schrödinger equation for a single electron in the potential of the "6-2" are expressed in elementary functions only in the case of certain relations between the parameters of the potential well, in other cases they are expressed in terms of Heun's functions. Found energy levels and electron wave functions in the ground state, and some low-lying states for the potential "6-2" for small values of the orbital angular momentum for the values of the parameters of the potential, when the solution of the Schrödinger equation is expressed in terms of elementary functions. A variational method for studying electron states for arbitrary values of the potential parameters, using the results as a starting solution. It is shown that this method allows to obtain the energy levels and wave functions of the ground state of an electron with sufficient accuracy for practical applications.

Keywords:

quantum rings, Hill potential, model potential, Schrodinger equation, Heun's functions

Acknowledgement

Работа выполнена при поддержке РФФИ и Министерства образования и науки Краснодарского края (13-01-96525).

Author Info

Evgeniy N. Tumayev

д-р физ.-мат. наук,заведующий кафедрой теоретической физики и компьютерных технологий Кубанского государственного университета

e-mail: tumayev@phys.kubsu.ru

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Issue

2016. No. 2

Pages

90-98

Submitted

2016-04-06

Published

2016-06-30

How to Cite

Tumayev E.N. The energy levels and wave functions of single-electron states in nano sized quantum rings. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2016, no. 2, pp. 90-98. (In Russian)

Copyright (c) 2016 Tumayev E.N.

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This work is licensed under a Creative Commons Attribution 4.0 International License.