Preprint Article Version 2 This version is not peer-reviewed

Superluminal Tunneling of a Relativistic Half-Integer Spin Particle through a Potential Barrier

Version 1 : Received: 3 May 2017 / Approved: 4 May 2017 / Online: 4 May 2017 (06:28:07 CEST)
Version 2 : Received: 13 July 2017 / Approved: 14 July 2017 / Online: 14 July 2017 (17:52:45 CEST)

How to cite: Nanni, L. Superluminal Tunneling of a Relativistic Half-Integer Spin Particle through a Potential Barrier. Preprints 2017, 2017050034 (doi: 10.20944/preprints201705.0034.v2). Nanni, L. Superluminal Tunneling of a Relativistic Half-Integer Spin Particle through a Potential Barrier. Preprints 2017, 2017050034 (doi: 10.20944/preprints201705.0034.v2).

Abstract

This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study’s results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.

Subject Areas

quantum tunneling; evanescent waves; Hartman effect; relativistic particles

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