|
| related topics |
| {time, wave, function} |
| {equation, function, exp} |
| {wave, scattering, interference} |
| {field, particle, equation} |
| {particle, mechanics, theory} |
| {bell, inequality, local} |
|
Low-energy relativistic effects and nonlocality in time-dependent
tunneling
Gaston Garcia-Calderon, Alberto Rubio, Jorge Villavicencio
abstract: We consider exact time-dependent analytic solutions to the Schr\"odinger
equation for tunneling in one dimension with cut off wave initial conditions at
$t=0$. We obtain that as soon as $t \neq 0$ 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0006110
- categories:
- quant-ph
- comments:
- 4 pages, 1 figure
- doi:
- 10.1103/PhysRevA.59.1758
- arxiv_id:
- quant-ph/0006110
- journal_ref:
- Phys. Rev. A 59 (3) 1758 (1999)
- created:
- 2000-06-24
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