Abstract
The quasi-one-dimensional scattering of a quantum particle on the two-dimensional δ-potential is considered. Analytical expressions for multi-channel transmission t n and reflection r n amplitudes are given. The problem is solved for the case of finite number of channels that is equal to N when the particle is incident on the potential while moving in l channel. The case of three-channel scattering was examined in details. As was shown within the frameworks of this problem, the “overpopulation” of particles in the second and third channels occurs when k 2 → 0 and k 3 → 0. The location points of δ-potential that provide the complete “overpopulation” of channels were also obtained.
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References
Landau, L.D. and Lifshitz, E.M., Quantum Mechanics, Non-Relativistic Theory, Pergamon Press, 1965.
Babikov, V.V., Metod fazovykh funktsii v kvantovoi mekhanike (Method of Phase Functions in Quantum Mechanics), Moscow: Nauka, 1976.
Azbel, M.Ya., Phys Rev. B, 1983, vol. 22, p. 4106.
Klyatskin, I.V., Metod pogruzheniya v teoriyu rasprostraneniya voln (Immersion method in the theory of wave propagation), Moscow: Nauka, 1986.
Aronov, A.G., Gasparian, V.M., and Gummuch, U., J. Phys. Condens. Matter, 1991, vol. 3, p. 3023.
Sedrakian, D.M., Badalyan, D.A., Gasparyan, V.M., and Khachatrian, A.Zh., ZETPh, 1996, vol. 109, p. 243; 1997, vol. 111, p. 575.
Sedrakian, D.M. and Khachatrian, A.Zh., Phys. Lett. A, 2000, vol. 265, p. 294.
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.
Sedrakian, D.M., Kazaryan, E.M., and Sedrakian, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2009, vol. 44, p. 257.
Sedrakian, D.M. and Sedrakian, L.R., Doklady NAS RA, 2010, vol. 110, p. 171.
Sedrakyan, D.M. and Sedrakyan, L.R., Phys. Sol. State, 2011, vol. 53, p. 1714.
Sedrakian, D.M., Bagdasaryan, A.Kh., and Sedrakyan, L.R., J. Contemp. Phys. (Armenian Ac. Sci.), 2015, vol. 50, p. 18.
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Original Russian Text © D.M. Sedrakian, D.H. Badalyan, L.R. Sedrakyan, 2015, published in Izvestiya NAN Armenii, Fizika, 2015, Vol. 50, No. 2, pp. 176–184.
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Sedrakian, D.M., Badalyan, D.H. & Sedrakyan, L.R. Multichannel scattering amplitudes of microparticles in a quantum well with two-dimensional δ-potential. J. Contemp. Phys. 50, 129–136 (2015). https://doi.org/10.3103/S1068337215020048
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DOI: https://doi.org/10.3103/S1068337215020048