Instantaneous tunneling of relativistic massive spin-0 particles

Theoretical Physics Group, National Institute of Physics University of the Philippines Diliman 1101 Quezon City, Philippines

^(a) E-mail: pmflores2@up.edu.ph (corresponding author)
^(b) E-mail: eagalapon@up.edu.ph

Received: 21 October 2022
Accepted: 21 December 2022

Abstract

The tunneling time problem studied earlier in Phys. Rev. Lett., 108 (2012) 170402, using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question whether instantaneous tunneling time is a consequence of using a non-relativistic 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 V_o is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepackets momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.