Spatio-temporal of Dirac and Klein Gordon particles in a one-dimensional box

TL;DR

This paper investigates the spatio-temporal behavior of Dirac and Klein-Gordon particles in a one-dimensional box, analyzing quantum carpets, revival times, and relativistic effects on these phenomena.

Contribution

It provides a comparative analysis of relativistic and non-relativistic quantum carpets and revival times for Dirac and Klein-Gordon particles in a confined system.

Findings

Relativistic effects decrease quantum carpet density.

Revival times are affected by relativistic phenomena.

Comparison of Dirac and Klein-Gordon particles' revival times.

Abstract

Present work is devoted to studying the spatio-temporal of the Dirac and the Klein Gordon (KG) particles confined in a one-dimensional box. We discuss the quantum carpets and revivals time for each particle. Moreover, we explain that the relativistic phenomena not only decrease the density of the corresponding carpets but also affect the revivals time of each particle within a box. Further, we impose different limiting conditions on the obtained Dirac energy solution and explain the wellknown slight-relativistic and non-relativistic quantum carpets, respectively. In addition, we extend our study to explain the quantum carpets of the KG particle at different energy states and compare its revivals time with the Dirac particle.