Relativistic quarks in one-dimensional periodic structures.

Abstract

We obtain the band condition for relativistic quarks moving in one-dimensional periodic potentials using the transfer matrix method. Using a strong electrostatic type of potential in the Dirac equation does not give confining properties, while Lorentz scalar potentials do. We give an analytic form for the wave function which results when the potential is taken to a delta function limit, and discuss the discrepancy between this result and that obtained by ``solving'' the Dirac equation for a delta function potential.