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

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

2004-04-09

arxiv.org/abs/quant-ph/0404057v1

Phys. Rev. A 69, 042704 (2004)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevA.69.042704

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 $\psi (x,t)$.

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