CONDITIONAL TIME-DELAY IN SCATTERING-THEORY

We give a general and mathematically precise definition of the notion of conditional time delay in scattering theory i.e., a notion of time delay for a given condition of observation of the scattered particle. A formula, generalising the Eisenbud-Wigner time delay formula, is der ived. The basic concept entering in the definition of the conditional time delay is that of conditional sojourn time. Although conditional s ojourn times cannot be uniquely defined in quantum mechanics because o f the uncertainty principle, we show that conditional time delays admi t a well defined probabilistic interpretation in the limit of infinitl y extended spatial regions. Some comments are presented in relation wi th the tunneling time problem.