The Lyapunov Exponents for Schrِdinger Operators with Slowly Oscillating Potentials

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator −d2/dx2+cos xνwith 0<ν<1 onL2[0, ∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.