Relativistic particle in a three-dimensional box

TL;DR

This paper extends the analysis of a Dirac particle confined in a three-dimensional box, examining relativistic effects and their impact on the density of states of a fermion gas.

Contribution

It provides a generalized solution for a Dirac particle in a 3D box, exploring both non-relativistic and ultra-relativistic limits with implications for fermion gases.

Findings

Box size influences the relativistic nature of low-lying states

Relativistic effects alter the density of states

Unified treatment of non-relativistic and ultra-relativistic regimes

Abstract

We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.