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