Geodesic
Propagation of wave packets through resonant quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 281-290

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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},
     publisher = {mathdoc},
     volume = {168},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a6/}
}
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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/