Major results of this thesis are the derivations of expressions for the proper operators measuring the two commonly accepted quantities concerning delay times in wave scattering, namely the dwell time and the group delay. We give the general forms of those operators for arbitrary scattering systems, not only flux conserving, but also systems featuring loss and gain.
The time delay operators may be used to generate a very special class of scattering states, featuring beam-like propagation patterns, following bundles of particle trajectories. We give an operational protocol to create such highly-collimated beams and we discuss the outcome for three different kinds of systems, which are flux-conserving systems, absorptive systems and so-called 'PT-symmetric' systems. The latter feature a very special arrangement of loss and gain regions, effecting that these systems remain invariant under the combined action of spatial reflection and time inversion.
In addition to the main results concerning delay times and beam-like scattering states, we also present in this thesis a highly feasible formulation of the coupling matrix for the investigated systems. This matrix can be used to construct the effective Hamiltonian, the scattering matrix and the dwell time operator. Our formulation, in contrast to previous expressions that can be found in the literature, enables a straight-forward numerical implementation and analytical usage.
Furthermore, we can provide an answer to the open question, what the link between the thresholds in the spectra of the scattering matrix and the Hamiltonian of the corresponding closed system, which depend on the strength of loss and gain in a PT-symmetric system, is.