in which formula_13 is the periodic part of the Bloch's theorem and the integral is over the Brillouin zone. Here index "n" refers to the "n"-th energy band in the crystal. The Wannier functions are localized near atomic sites, like atomic orbitals, but being defined in terms of Bloch functions they are accurately related to solutions based upon the crystal potential. Wannier functions on different atomic sites R are orthogonal. The Wannier functions can be used to form the Schrödinger solution for the "n"-th energy band as: