Relativistic particle in a three-dimensional box

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.

v1: 8 pages, 2 figures, revtex4; v2: minor typos corrected to match published version in Phys. Lett. A

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