Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

TL;DR

This paper develops a relativistic time-of-arrival operator for spin-0 particles and demonstrates that tunneling can be instantaneous, highlighting a fundamental quantum effect in relativistic quantum mechanics.

Contribution

It introduces a quantized relativistic time-of-arrival operator using modified Weyl-ordering and analyzes tunneling times for relativistic particles.

Findings

Tunneling time is instantaneous when barrier height is below rest mass energy.

The approach uses a modified Weyl-ordering rule for quantization.

Instantaneous tunneling is identified as an inherent quantum phenomenon.

Abstract

We provide a full account of our recent report (EPL, 141 (2023) 10001}) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a square barrier. It was shown that the tunneling time of a relativistic spin-0 particle is instantaneous under the condition that the barrier height $V_o$ is less than the rest mass energy. This implies that instantaneous tunneling is an inherent quantum effect in the context of arrival times.