Quantum mechanical time-delay matrix in chaotic scattering

We calculate the probability distribution of the matrix Q = -i (h) over bar S(-1)partial derivative S/partial derivative E for a chaotic system with scattering matrix S at energy E. The eigenvalues tau(j) of Q are the so-called proper delay times, introduced by Wigner and Smith to describe the time dependence of a scattering process. The distribution of the inverse delay times turns out to be given by the Laguerre ensemble from random-matrix theory.