  We present the analytical solution of the wavefunction and energy dispersion
of armchair graphene nanoribbons (GNRs) based on the tight-binding
approximation. By imposing hard-wall boundary condition, we find that the
wavevector in the confined direction is discretized. This discrete wavevector
serves as the index of different subbands. Our analytical solutions of
wavefunction and associated energy dispersion reproduce the numerical
tight-binding results and the solutions based on the k*p approximation. In
addition, we also find that all armchair GNRs with edge deformation have energy
gaps, which agrees with recently reported first-principles calculations.
