Geodesic
Propagation of wave packets through resonant quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 281-290 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We use a previously proposed modified saddle point method to describe the tunneling of a rectangular wave packet through a resonant quantum system. We calculate the shape of the wave packet obtained at the quantum system output analytically for different values of the level width. The result of propagation is a wave packet that is the superposition of complementary error functions. Comparing the result with the exact numerical solution obtained without using any asymptotic methods shows a rather good coincidence. We study the propagation of Gaussian and rectangular wave packets in detail for large values of the resonance level width.
Keywords: tunneling, resonance level, wave packet, resonance scattering, quantum system, scattering matrix. 
@article{TMF_2011_168_2_a6,
     author = {N. A. Ivanov and V. V. Skalozub},
     title = {Propagation of wave packets through resonant quantum systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {281--290},
     year = {2011},
     volume = {168},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a6/}
}
TY  - JOUR
AU  - N. A. Ivanov
AU  - V. V. Skalozub
TI  - Propagation of wave packets through resonant quantum systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 281
EP  - 290
VL  - 168
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a6/
LA  - ru
ID  - TMF_2011_168_2_a6
ER  - 
%0 Journal Article
%A N. A. Ivanov
%A V. V. Skalozub
%T Propagation of wave packets through resonant quantum systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 281-290
%V 168
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a6/
%G ru
%F TMF_2011_168_2_a6
N. A. Ivanov; V. V. Skalozub. Propagation of wave packets through resonant quantum systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 281-290. http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a6/

[1] M. Razavy, Quantum Theory of Tunneling, World Sci., Singapore, 2003 | Zbl

[2] H. Mizuta, M. Tanoue, The Physics and Applications of Resonant Tunneling Diodes, Cambridge Univ. Press, Cambridge, 1995

[3] U. Wulf, E. R. Racec, P. N. Racec, A. Aldea, Mat. Sci. Eng. C, 23:6–8 (2003), 675–681 | DOI

[4] A. I. Baz, Ya. B. Zeldovich, A. M. Perelomov, Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, Nauka, M., 1971

[5] U. Wulf, V. Skalozub, A. Zaharov, Phys. Rev. B, 77:4 (2004), 045318, 7 pp. | DOI

[6] L. Brillouin, Wave Propagation and Group Velocity, Acad. Press, New York, 1960 | MR | Zbl

[7] L. E. Ballentine, Quantum Mechanics. A Modern Development, World Scientific, Singapore, 1998 | MR | Zbl

[8] M. A. Lavrentev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973 | MR | Zbl