Comment on ‘‘Energy-band equation for a general periodic potential’’

The authors wish to comment on a recent publication on energy-band equations [Phys. Rev. B 36, 1378 (1987)]. In particular, this paper introduces an invalid hypothesis that leads its authors to conclude that the generalized band theory previously derived and tested by us is in error, and that its equations represent a necessary but not a sufficient condition on the solution. The Bloch symmetrized multipolar representation introduced in this paper on the basis of this hypothesis is overdetermined and hence is zero (the trivial representation). We offer an explicit counterexample to the fundamental hypothesis of this paper. Finally we show by construction that the exact solution to the empty-lattice problem is certainly a solution to the linear equations of our theory, and since these equations (as well-defined functionals of E and k) do not have multiple solutions, we conclude that our method exactly solves the empty-lattice problem.