This Demonstration explores the solutions of the secular equations for graphene nanoribbons with zigzag and bearded edges. For graphene nanoribbons with zigzag edges, the secular equation is

, while for a ribbon with bearded edges it is

. For ribbons containing

pairs of carbon atoms in their unit cells, these equations quantize the transverse momentum of the electron,

, and couple it to the longitudinal momentum,

. The equation for a ribbon with zigzag edges is the same as equation (19) in [1]. The equation for a ribbon with bearded edges,

, is different from the equation

given in reference [2]. The sign in front of the second term is of no physical importance, but the minus is more convenient for mathematical treatment, as has been discussed for zigzag ribbons [1].