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

Manabu Miyamoto
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Abstract

The long time behavior of scattered wave packets $ψ(x,t)$ from a finite-range potential is investigated, by assuming $ψ(x,t)$ to be initially located outside the potential. It is then shown that $ψ(x,t)$ 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 $ψ(x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $ψ(x,t)$.

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Manabu Miyamoto. 2004-04-09. Initial wave packets and the various power-law decreases of scattered wave packets at long times. https://doi.org/10.1103/physreva.69.042704

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