  We extend a result on dispersion for solutions of the linear Schr\"odinger
equation, proved by Firsova for operators with finitely many energy bands only,
to the case of smooth potentials in 1D with infinitely many bands. The proof
consists in an application of the method of stationary phase. Estimates for the
phases, essentially the band functions, follow from work by Korotyaev. Most of
the paper is devoted to bounds for the Bloch functions. For these bounds we
need a detailed analysis of the quasimomentum function and the uniformization
of the inverse of the quasimomentum function
