Time delay for dispersive systems in quantum scattering theory. I. The Friedrichs model

TL;DR

This paper introduces a method to establish the existence and equivalence of time delay in quantum scattering, specifically within the Friedrichs model and finite rank potentials, enhancing understanding of scattering processes.

Contribution

It provides a new approach to prove the existence and identity of time delay in quantum scattering models, applicable to finite rank potentials.

Findings

Established the existence of time delay in the Friedrichs model

Proved the identity of time delay with Eisenbud-Wigner time delay

Applicable to scattering by finite rank potentials

Abstract

We present a method for proving the existence of time delay (defined in terms of sojourn times) as well as its identity with Eisenbud-Wigner time delay in the case of the Friedrichs model. We show that this method applies to scattering by finite rank potentials.