  A theory of electron states for graphene nanoribbons with a smoothly varying
width is developed. It is demonstrated that the standard adiabatic
approximation allowing to neglect the mixing of different standing waves is
more restrictive for the massless Dirac fermions in graphene than for the
conventional electron gas. For the case of zigzag boundary conditions, one can
expect a well-pronounced conductance quantization only for highly excited
states. This difference is related to the relativistic Zitterbewegung effect in
graphene.
