2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56555In this article we prove an upper bound for the Lyapunov exponent $γ(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schrödinger operators in one dimension. These Schrödinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $γ(E)$ and $N(E)-\sqrt{E}/π$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.9 pagesMathematical Physics(2000 Revision) 82B44; 34F05; 60H25text