Discontinuities in Dirac eigenfunction expansions

Abstract

An expansion, over a finite interval, of a two-component function in a basis of eigenfunctions of a one-dimensional regular Dirac differential operator with separated homogeneous boundary conditions imposed at ends of the interval is considered. It is shown that at the ends of the domain the expansion does not converge to the expanded function unless the latter obeys at these points the same homogeneous boundary conditions as the basis eigenfunctions. General results obtained in the work are illustrated by an analytically solvable example. The problem is related to the R-matrix theory for Dirac particles.