The generalized Lyapunov exponent for the one-dimensional Schrödinger equation with Cauchy disorder: some exact results

Alain Comtet, Christophe Texier, Yves Tourigny

We consider the one-dimensional Schrödinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function $\psi (x)$, known in the l…