These eigenstates are written with subscripts as formula_7, where formula_8 is a discrete index, called the band index, which is present because there are many different wave functions with the same formula_4 (each has a different periodic component formula_3). Within a band (i.e., for fixed formula_8), formula_7 varies continuously with formula_4, as does its energy. Also, formula_7, is unique only up to a constant reciprocal lattice vector formula_15, or, formula_16. Therefore, the wave vector formula_4 can be restricted to the first Brillouin zone of the reciprocal lattice without loss of generality.