The asymptotic behaviour of wannier functions

Abstract

Abstract The treatment of many problems in electron theory is considerably simplified if the Wannier representation is used, provided the Wannier functions are well localized and decrease exponentially for large distances from their centres. It is shown that in the case of band groups with point and line degeneracies it is possible to define pseudo‐Wannier functions with exponential tails, which everywhere in the crystal deviate as little from conventionally defined Wannier functions as one wants. The question how far the Wannier functions extend with appreciable magnitude from their centres into the crystal is not considered.