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Time‐dependent investigation of the resonant tunneling in a double‐barrier quantum well
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9.A typical value we use for σ is 550 Å and the tail of the initial wave packet is truncated at a distance away from the center of the packet. This center is initially located at a position such that the truncated tail is a few hundred angströms to the left of the double‐barrier structure. The time scales discussed in the text are not very sensitive to the initial packet conditions, as long as is reasonably small compared with They also depend very little on the initial position of the wave packet.
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11.L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non‐relativistic Theory), 3rd ed. (Pergamon, New York, 1987). We computed as the full width at half‐maximum of the peak in the one‐dimensional transmission coefficient by integrating the time‐independent Schrödinger equation.
12.The definition of this time is somewhat arbitrary. We define it as the period of time from when the total probability in the first barrier reached a few percent of until
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15.In general the time scales for a three‐dimensional system could be different from those of a one‐dimensional system. But in the current case there is a translational invariance in the plane parallel to the barrier which reduces the problem effectively to one‐dimension.
16.In obtaining these values we assume that the tunneling is via the γ point of the AlAs barriers, as was also done by the authors of Ref. 6. However, as mentioned in the text, one may have to consider the effect of the mixing for these barriers.
17.E. H. Hauge, J. P. Falck, and T. A. Fjeldly, Phys. Rev. B 36, 4203 (1987).
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