Scipio Cuccagna
Dispersion for Schr\"odinger equation with
periodic potential in 1D
(95K, tex)
ABSTRACT. 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.