New electron wave functions at the center of the Brillouin zone are given for the valence and conduction bands of semiconductor crystals with diamond and zinc-blende lattice symmetries. They are analyzed in the absence of spin-orbit coupling and take into account the lack of inversion symmetry in zinc-blende lattices compared to diamond ones. For this reason, our wave functions differ from the traditionally used ones. In particular, for zinc-blende symmetry crystals, they provide nonvanishing intravalence band matrix elements of momentum p in accordance with group theory selection rules.