Charge transfer on a two-dimensional lattice with Tamm states

We consider the quantum dynamics of charge propagation over a two-dimensional lattice with impurity sites at the lattice edges. These sites simulate boundary $($Tamm$)$ states. We solve the nonstationary problem of the evolution of a quantum excitation over impurity sites at the lattice perimeter in the tight-binding approximation. We obtain the solution as an expansion in eigenfunctions of the unperturbed system Hamiltonian. We obtain analytically accurate results for the propagation of the wave function over impurity sites.