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 derived. The basic concept entering in the definition of the conditional time delay is that of conditional sojourn time. Although conditional sojourn times cannot be uniquely defined in quantum mechanics because of the uncertainty principle, we show that conditional time delays admit a well defined probabilistic interpretation in the limit of infinitly extended spatial regions. Some comments are presented in relation with the tunneling time problem.

Sassoli de Bianchi, M. (1993). Conditional time-delay in scattering theory. Helv. Phys. Acta 66, pp. 361-377. Doi: 10.5169/seals-116575.