Instantaneous tunneling of relativistic massive spin-0 particles

Abstract

The tunneling time problem earlier studied in Phys. Rev. Lett. 108, 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous tunneling time is a consequence of using a nonrelativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA-operators for spin-0 particles in the presence of an interaction potential V (q) via quantization. We then construct the corresponding barrier traversal time operator and impose the condition that the barrier height Vo is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepacket’s momentum distribution contributes to the barrier traversal time while the below-barrier components are transmitted instantaneously.