Comment on "Extended Wannier-Slater theorem for graded mixed semiconductors"

We carefully review the derivation of the extended Wannier-Slater theorem describing the behavior of charges in graded mixed semiconductors. In situations where the grading function and the external potential-energy function change very slowly with position we show that the resulting effective-mass-like equation (with position-dependent mass) for the envelope function is essentially unique. Limits of applicability of this equation are pointed out.