Angular time delay in quantum mechanical scattering

TL;DR

This paper explores angular time delay in quantum scattering, re-derives key formulas, clarifies conceptual issues, and applies the concepts to scattering off a hard sphere, highlighting observable effects in diffraction regions.

Contribution

It provides a new derivation and clarification of quantum angular time delay and space shift, connecting them to classical analogs and applying them to a specific scattering example.

Findings

Pronounced peaks in time delay and space shift at diffraction minima

Clarification of conceptual issues in quantum scattering time delay

Potential observability of effects in short wavelength scattering

Abstract

We apply Brunetti and Fredenhagen's [Phys. Rev. A 66 (2002) 044101] concept of the time of occurrence of an event in quantum mechanics to the example of scattering off a spherical potential. Thereby, we re-derive the expression of Froissart, Goldberger, and Watson [Phys. Rev. 131 (1963) 2820] for the angular time delay, clarifying some conceptual issues with their derivation. We also present an elementary re-derivation of the "space shift" (essentially the impact parameter) defined in the quantum mechanical context by the same authors. We clarify the relation of both quantities to their classical counterparts in the context of the WKB approximation. As an example, we apply the concepts to scattering at a hard sphere. We find pronounced peaks in the both the time delay and the space shift at the minima of intensity in the forward diffraction region for short wavelength scattering and discuss whether these could in principle be observable.