Impedance models of double well structures
DOI:
https://doi.org/10.20535/RADAP.2015.60.131-140Keywords:
double well structure, impedance delta-inhomogeneity, input impedanceAbstract
Introduction. In this paper the impedance models double well structures (DWS) which is based on δ-inhomogeneities and rectangular potential are developed. The models of double well potential which is based on δ-functions and rectangular depending allow to obtain analytical solutions and to investigate important features of DWS.Analogy of double well structure and coupled oscillatory circuits. The analogy of DWS and coupled oscillatory circuits are considered. It is presented comparison the Schrödinger equation for the wave function and the equation for the current circuit without loss. It is shown that DWS as the system with two states performs the function of logical operations similar bits in classical computer.
Models based on the impedance δ-inhomogeneities. Two models of DWS based on the impedance δ-inhomogeneities: δ-barrier in the potential well and two δ-wells are developed. The analytical expressions for input impedance and eigenvalues are received and investigated. It is shown that characteristics of DWS with finite size and δ-inhomogeneities agree well.
Eigenvalues of asymmetric double well structure. The most general case of asymmetric DWS with a rectangular potential is considered. The eigenvalues of such a structure on the basis of a generalized model of barrier structures are found. Dependences of eigenvalues of symmetric and asymmetric DWS are presented.
Conclusions. Impedance models allow to obtain the analytical solutions with substantial generalization problems in comparison with known traditionally solved problems. By analysis of input impedance characteristics conditions for the eigenvalues DWS placed between environments with different wave impedance are received.
References
Перелік посилань
Фейнман Р. Фенмановские лекции по физике. Квантовая механика (вып. 8, 9) / Р. Фейнман, Р. Лейтон, М. Сэндс. – М. : Мир. – 1978. – 524 с.
Jelic V. The double well potential in quantum mechanics: a simple, numerically exact formulation / V. Jelic, F. Marsiglio // Eur. J Phys. – 2012. – Vol. 33, No. 6. – P. 1651-1666.
Hasegawa H. Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials / H. Hasegawa // Physica E. – 2014. – Vol. 59. – P. 192-201.
Markos P. Wave Propagation From Electrons to Photonic Crystals and Left-Handed Materials / P. Markos, C. M. Soukoulis. – Princeton and Oxford: Princeton University Press, 2008. – 352 p.
Basdevant J.-L. Lectures on Quantum Mechanics. / J. L. Basdevant. – N. Y. : Springer, 2007. – 308 р.
Khondker A. N. Transmission line analogy of resonance tunneling phenomena: the generalized іmpedance concept / A. N. Khondker, M. R. Khan, A. F. M. J. Anwar // J. Appl. Phys. – 1988. – Vol. 63, No. 10. – P. 5191-5193.
Нелин Е. А. Импедансная модель для “барьерных” задач квантовой механики / Е. А. Нелин // УФН. – 2007. – Т. 177, №3. – С. 307-313.
Нелін Є.А. Квантово-механічні структури з дельта-функціональним потенціалом / Є.А. Нелін, М.В. Водолазька // Наукові вісті НТУУ "КПІ". - 2013. - № 4. - с. 137-144.
Спроул Р. Современная физика / Р. Спроул. – М. : Наука, 1974. – 296 с.
Валиев К. А. Квантовые компьютеры и квантовые вычисления / К. А. Валиев // УФН. – 2005. – Т. 175, № 1. – С. 3–39.
Менский М. Б. Квантовая механика: новые эксперименты, новые приложения и новые формулировки старых вопросов / М. Б. Менский // УФН. – 2000. – Т. 170, № 6. – С. 631-648.
Водолазская М. В. Модель импедансных дельта-неоднородностей для микро- и наноструктур / М. В. Водолазская, Е. А. Нелин // Известия вузов. Радиоэлектроника. – 2014. – Т. 57, № 5. – С. 25-34.
Нелин Е. А. Импедансные условия резонансного прохождения и резонансной локализации волн в барьерных структурах / Е. А. Нелин // ЖТФ. – 2011. – Т. 81, № 1. – С. 137-139.
Галицкий В. М. Задачи по квантовой механике // В. М. Галицкий, Б. М. Карнаков, В. И. Коган. – М. : Наука, 1981. – 658 с.
References
Feinman R., Leiton R. and Sends M. (1978) Fenmanovskie lektsii po fizike. Kvantovaya mekhanika (vyp. 8, 9) [Fenman’s lectures on physics. Quantum mechanics (Vol. 8, 9)]. Moscow, Mir Publ, 524 p.
Jelic V. and Marsiglio F. (2012) The double well potential in quantum mechanics: a simple, numerically exact formulation. Eur. J Phys., vol. 33, no. 6, pp. 1651–1666.
Hasegawa H. (2014) Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials. Physica E., vol. 59, pp. 192–201.
Markos P. and Soukoulis C. M. (2008) Wave Propagation From Electrons to Photonic Crystals and Left-Handed Materials. Princeton and Oxford: Princeton University Press, 352 p.
Basdevant J.-L. (2007) Lectures on Quantum Mechanics. New York, Springer, 308 р.
Khondker A. N., Khan M. R. and Anwar A. F. M. J. (1988) Transmission line analogy of resonance tunneling phenomena: the generalized іmpedance concept. J. Appl. Phys., vol. 63, no. 10, pp. 5191–5193.
Nelin E.A. (2007) Impedance model for quantum-mechanical barrier problems. Phys. Usp., vol. 50, no. 3, pp. 293-299.
Nelin E.A. and Vodolazska M.V. (2013) Quantum-Mechanical Structures with Delta-Functional Potential. Naukovi visti NTUU KPI, no. 4, pp. 137-144.
Sproul R. (1974) Sovremennaya fizika [Modern physics]. Moskow, Nauka, 296 p.
Valiev K. A. (2005) Quantum computers and quantum computations. Phys. Usp., vol. 48, pp. 1 – 36.
Menskii M. B. (2000) Quantum mechanics: new experiments, new applications, and new formulations of old questions. Phys. Usp., vol. 43, pp. 585- 600.
Vodolazka, M. and Nelin, E. (2014) Model of impedance delta-inhomogeneities for micro- and nanostructures. Radioelectronics and Communications Systems. Vol. 57, No 5. pp. 208-216.
Nelin E. A. (2011) Impedance conditions for resonance propagation and resonance localization of waves in barrier structures. Technical Physic., vol. 56, no. 1, pp. 132-134.
Galitskii V. M., Karnakov B. M. and Kogan V. I. (1981) Zadachi po kvantovoi mekhanike [Tasks on quantum mechanics]. Moscow, Nauka, 658 p.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
