Physics – Quantum Physics
Scientific paper
2000-06-10
Physical Review B Rapid Communications 60, R2142 (1999)
Physics
Quantum Physics
4 pages, 2 figures
Scientific paper
10.1103/PhysRevB.60.R2142
The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.
Romo Roberto
Villavicencio Jorge
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