Initial wave packets and the various power-law decreases of scattered wave packets at long times

Abstract

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.

5 pages, 1 figure

References in corpus (3)

• Asymptotic behaviour of the probability density in one dimension
• The various power decays of the survival probability at long times for free quantum particle
• Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

Cited by in corpus (5)

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• Transient effects and reconstruction of the energy spectra in the time evolution of transmitted Gaussian wave packets
• Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
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• Time Evolution of a Decaying Quantum State: Evaluation and Onset of Non-Exponential Decay