Quantum Mechanical Time-Delay Matrix in Chaotic Scattering

We calculate the probability distribution of the matrix Q=-i{h_bar}S{sup -1}{partial_derivative}S/{partial_derivative}E for a chaotic system with scattering matrix S at energy E . The eigenvalues {tau}{sub 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. {copyright} {ital 1997} {ital The American Physical Society}