Artifacts of grid-based electron structure calculations

Electron structure calculations over equidistant grids represent physical observables by matrices usually chosen as the projection of the corresponding operator in the Schrِdinger picture onto the subspace expanded by the basis set of the given grid resolution. It is shown that any matrix representation compatible with the translational symmetry of the lattice suffers from essential difficulties. Especially the momentum and related operators like the kinetic energy show anomalous behavior, moreover, the required canonical commutation relation can never be satisfied.