  Solutions of the one dimensional Dirac equation with piece-wise constant
potentials are presented using standard methods. These solutions show that the
Klein Paradox is non-existent and represents a failure to correctly match
solutions across a step potential. Consequences of this exact solution are
studied for the step potential and a square barrier. Characteristics of
massless Dirac states and the momentum linear band energies for Graphene are
shown to have quite different current and momentum properties.
