Comment on "Bound states of edge dislocations: The quantum dipole problem in two dimensions"

Abstract

We show that the numerical results contained in a recent paper are affected by a non optimal implementation of the methods which have been used to obtain these results. A careful analysis done using the Rayleigh-Ritz method provides a rigorous upper bound for the energy of the ground state of an electron in a two dimensional potential generated by the edge dislocation, as well as precise values for the excited states. The extrapolation of the results corresponding to different subspaces is used to obtain a precise estimate of the fundamental energy of the model. The energies of the first 500 states that we have calculated are in perfect agreement with the expected asymptotic behavior.