  We provide an exact analytical technique to obtain within a lattice model the
wave functions of the edge states in zigzag- and bearded-edge graphene, as well
as of the Fermi-arc surface states in Weyl semimetals described by a minimal
bulk model. We model the corresponding boundaries as an infinite scalar
potential localized on a line, and respectively within a plane. We use the
T-matrix formalism to obtain the dispersion and the spatial distribution of the
corresponding boundary modes. Furthermore, to demonstrate the power of our
approach, we write down the surface Green's function of the considered Weyl
semimetal model, and we calculate the quasiparticle interference patterns
originating from an impurity localized at the respective surface.
