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Low-energy relativistic effects and nonlocality in time-dependent tunneling | | Gaston Garcia-Calderon
; Alberto Rubio
; Jorge Villavicencio
; | | Date: |
24 Jun 2000 | | Journal: | Phys. Rev. A 59 (3) 1758 (1999) | | Subject: | quant-ph | | Affiliation: | Instituto de Fisica, Universidad Nacional Autonoma de Mexico), Alberto Rubio (Facultad de Ciencias, Universidad Autonoma de Baja California) and Jorge Villavicencio (Centro de Investigacion Cientifica y de Educacion Superior de Ensenada | | Abstract: | We consider exact time-dependent analytic solutions to the Schrödinger equation for tunneling in one dimension with cut off wave initial conditions at $t=0$. We obtain that as soon as $t
eq 0$ the transmitted probability density at any arbitrary distance rises instantaneously with time in a linear manner. Using a simple model we find that the above nonlocal effect of the time-dependent solution is suppressed by consideration of low-energy relativistic effects. Hence at a distance $x_0$ from the potential the probability density rises after a time $t_0=x_0/c$ restoring Einstein causality. This implies that the tunneling time of a particle can never be zero. | | Source: | arXiv, quant-ph/0006110 | | Services: | Forum | Review | PDF | Favorites | |
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