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# Title: Tunneling dynamics in relativistic and nonrelativistic wave equations

Abstract: We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cut-off. A scaling of position and time reduces to a single case all the (below cut-off) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different shallow'' and deep'' tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or B\"uttiker-Landauer) time "tau". The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle point contributions, and may be characterized by two times for the arrival of the maxima of lower and upper envelops. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation.
 Subjects: Quantum Physics (quant-ph) DOI: 10.1103/PhysRevA.68.032101 Cite as: arXiv:quant-ph/0303133 (or arXiv:quant-ph/0303133v1 for this version)

## Submission history

From: J. G. Muga [view email]
[v1] Fri, 21 Mar 2003 11:05:31 GMT (217kb)