We present a consistent continuum description of finite graphene nanoribbons within the Dirac Hamiltonian formalism, addressing the interplay between geometry and boundary conditions. Although effective Dirac models are widely used to describe low-energy electronic properties, their application to finite systems requires systematic treatment of boundary-condition compatibility. We show that boundary conditions associated with zigzag and armchair edges cannot, in general, be imposed independently in a finite geometry. Their simultaneous implementation introduces nontrivial constraints that define a well-posed spectral problem. Within the consistent framework developed here, we derive the complete set of admissible solutions, including both oscillatory and edge-localized states. We demonstrate that the spectrum organizes into valley-coupled modes with identical eigenenergies, and that the existence of edge-localized states is restricted to specific regions of the spectral parameter space, depending explicitly on the system size. Furthermore, we show that different but unitarily equivalent forms of the Dirac Hamiltonian become physically inequivalent once boundary conditions are imposed, as they induce distinct constraints on the wavefunction components. To validate our analytical framework, we perform extensive numerical comparisons with tight-binding calculations on the honeycomb lattice. The results obtained here confirm that our consistent boundary-condition implementation correctly captures the physics of both zigzag and armchair terminations, including the absence of topologically protected edge states in armchair geometries. Our results establish precise criteria for the consistent application of continuum models to finite graphene nanoribbons and clarify the role of boundary conditions in their electronic structure.

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• Confinement
• Dirac equation
• Dirac fermions
• Edge states
• Mesoscopics
• Graphene