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This article is cited in 1 scientific paper (total in 1 paper)
Propagation of wave fronts
Evolution of a wave packet scattered by a one-dimensional potential
A. Zh. Khachatriana, A. G. Alexanyanb, V. A. Khoetsyana, N. A. Alexanyana a State Engineering University of Armenia, Yerevan
b Institute of Applied Problems of Physics of the National Academy of Sciences of the Republic of Armenia, Yerevan
Abstract:
We consider the evolution of a wave packet that is made up of a group of the wave functions describing the stationary scattering process and tunnels through a one-dimensional potential of arbitrary form. As the main characteristics of the time difference of the tunnelling process, use is made of the propagation speed of the wave-packet maximum. We show that the known Hartman formula for the tunnelling time corresponds to the wave packet with a wavenumber-uniform spectral composition in the case, when the phase and transmission coefficient modulus dispersions are taken into account only in the linear approximation. The amplitude of the main peak of the transmitted wave intensity is proven to be independent of the tunnelling time and is determined by the transmission coefficient of the spectral component at the carrier frequency and the spectral width of the wave packet. In the limit of an infinitely wide potential barrier the amplitude of the wave-packet maximum is shown to tend to zero slower than the tunnelling time tends to its asymptotic value, i.e., indeed we deal with the paradox of an infinitely large propagation speed of a wave disturbance through the barrier.
Keywords:
wave packet, tunnelling, Hartman effect.
Received: 22.09.2012 Revised: 07.12.2012
Citation:
A. Zh. Khachatrian, A. G. Alexanyan, V. A. Khoetsyan, N. A. Alexanyan, “Evolution of a wave packet scattered by a one-dimensional potential”, Kvantovaya Elektronika, 43:6 (2013), 574–581 [Quantum Electron., 43:6 (2013), 574–581]
Linking options:
https://www.mathnet.ru/eng/qe15002 https://www.mathnet.ru/eng/qe/v43/i6/p574
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