The delay time operator for simple scattering systems

Philippe Martin

X.P. Wang

J. M. Jauch, Kalyan B. Sinha, Baidyanath Misra

The relation between time-delay and the phase-shift operator is derived in the context of the time-dependent scattering theory for simple (single channel) scattering systems. The sufficient conditions on the interaction under which this relation can be established in a mathematical correct manner are formulated and the precise sense in which this relation can be interpreted is discussed. The results obtained here generalize and unify various partial results previously published on this subject.

Hanns Georg Kilian

Abstract We propose and discuss an operative definition of the notion of a mean collision time delay within the frame of non‐relativistic time‐dependent quantum scattering theory. As an application we calculate the collision time delay for two simple but interesting examples which permit us to make a preliminary calculation of the lifetime of a decaying compound system.

W. van Dijk, Ken Kiers A

The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.

Arne Jensen