Abstract
The penetration of the microparticle (electron) through the δ-potential barriers which are embedded into the quantum wire of cylindrical shape with the characteristic effect of dimensional quantization in the transverse direction is considered. The analytical expressions for the amplitudes of the multichannel scattering, which are valid for the barriers consisting of one and two δ-potentials located at some distance from each other are obtained. It is shown that the multichannel scattering turns into the one-dimensional, if the initial energy of the longitudinal motion of electron is not sufficient to excite the higher channels of scattering. In this case, the obtained formulas for the scattering amplitudes coincide with the well-known expressions for the one-dimensional scattering. The obtained solutions satisfy the conservation law of the number of particles, which is the indirect proof of the validity of derived formulas.
Similar content being viewed by others
References
Harrison, P., Quantum Wells, Wires and Dots. Theoretical and Computational Physics, New York Wiley and Sons, 2005.
Boese, D., Lischka, M., and Reichl, L.E., Phys. Rev. B, 2000, vol. 62, p. 16933.
Souma, S. and Suzuki, A., Phys. Rev. B, 2002, vol. 65, p. 115307.
Prior, J., Somoza, A.M., and Ortuno, M., Phys. Rev. B, 2005, vol. 72, p. 024206.
Sedrakian, D.M., Kazaryan, E.M, and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2009, vol. 44, p. 257.
Babikov, V.V., Metod fazovykh funktsiy v kvantovoi mekhanike (The Method of Phase Functions in Quantum Mechanics), Moscow Nauka, 1976.
Klyatskin, V.I., Metod pogruzheniya v teorii rasprostraneniya voln (The Immersion Method in the Theory of Wave Propagation), Moscow Nauka, 1986.
Sedrakian, D.M., Kazaryan, E.M., and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2010, vol. 45, p. 111.
Sedrakian, D.M., Kazaryan, E.M., and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2011, vol. 46, p. 11.
Sedrakian, D.M., Badalyan, D.H., and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2012, vol. 47, p. 99.
Sedrakyan, D.M. and Sedrakyan, L.R., Phys. Sol. State, 2011, vol. 53, p. 1714.
Sedrakian, D.M., Badalyan, D.A., and Sedrakyan, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2014, vol. 49, p. 43.
Sedrakian, D.M. and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2014, vol. 49, p. 209.
Sedrakian, D.M., Badalyan, D.H., and Sedrakyan, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2015, vol. 50, p. 129.
Flügge, S., Practical Quantum Mechanics, Springer Science & Business Media, 2012.
Sedrakian, D.M., J. Contemp. Phys. (Armenian Ac. Sci.), 2010, vol. 45, p. 25.
Sedrakian, D.M., J. Contemp. Phys. (Armenian Ac. Sci.), 2010, vol. 45, p. 118.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.M. Sedrakian, D.H. Badalyan, A.Yu. Aleksanyan, 2016, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Fizika, 2016, Vol. 51, No. 4, pp. 452–463.
About this article
Cite this article
Sedrakian, D.M., Badalyan, D.H. & Aleksanyan, A.Y. Multichannel scattering amplitudes of microparticle in a quantum wire with three-dimensional δ-potentials. J. Contemp. Phys. 51, 335–344 (2016). https://doi.org/10.3103/S1068337216040058
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068337216040058