  Structure and coordinate dependence of the reflected wave, as well as
boundary conditions for quasi-particles of graphene and the two dimensional
electron gas in sheets with abrupt lattice edges are obtained and analyzed by
the Green's function technique. In particular, the reflection wave function
contains terms inversely proportional to the distance to the graphene lattice
edge. The Dirac equation and the momentum dependence of the wave functions of
the quasi-particles near the conical points are also found by the perturbation
theory with degeneracy in terms of the Bloch functions taken at the degeneracy
points. The developed approach allows to formulated the validity criteria for
the Dirac equation in a rather simple way.
