# Topological quantum edge states

We studied the propagation of waves described by Schrödinger’s equation along the interface between two periodic structures (edge states) using numerical and analytical methods. Specifically, we considered the interface between different configurations of the Haldane model, which can exist in topological' and non-topological’ phases.  After first studying a simplified one-dimensional model, we worked out the correct Hamiltonian operator for the two-dimensional system, diagonalized it numerically, and then used this information to integrate the Schrödinger equation for different initial conditions. Our computations showed that wave packets propagating along the interface between two distinct 'non-topological’ configurations are reflected by defects’ of the interface, whereas wave packets propagating along the interface between topological’ and `non-topological’ configurations propagate past defects almost unaffected.