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A Bravais-lattice operator is defined in one band of a solid. Its eigenstates are covariantly defined Wannier functions and its eigenvalues are all the points of the Bravais lattice. This operator establishes a convenient phase convention for Bloch functions. The newly defined Bravais-lattice operator is conjugate to the quasimomentum and together they form a complete set of operators by means of which any one-band operator can be expressed. The Wannier functions for different bands and sites are shown to be eigenfunctions of a band index and the Bravais-lattice operators. It is shown that the one-band position operator has a discrete spectrum with the structure of a Stark ladder in solids. A kq representation is defined for one band which leads to symmetric coordinates for superlattices. The conjugate operators to these symmetric coordinates form the superlattice representation of McIrvine and Overhauser.
J. Žák (Sat,) studied this question.