General boundary conditions for a Dirac particle in a box and their non-relativistic limits

Abstract

The most general relativistic boundary conditions (BCs) for a `free' Dirac particle in a one-dimensional box are discussed. It is verified that in the Weyl representation there is only one family of BCs, labelled with four parameters. This family splits into three sub-families in the Dirac representation. The energy eigenvalues as well as the corresponding non-relativistic limits of all these results are obtained. The BCs which are symmetric under space inversion P and those which are CPT invariant for a particle confined in a box, are singled out.