# Quantum scattering with semiclassical asymptotic motion

## TL;DR

This paper enhances quantum scattering theory by incorporating semiclassical propagators, allowing the wave function to exhibit classical trajectories at macroscopic distances, bridging quantum and classical descriptions.

## Contribution

It introduces semiclassical propagators into quantum scattering theory to explicitly include classical trajectories in asymptotic wave functions.

## Key findings

- Derivation of the asymptotic Kemble imaging theorem (IT) limit.
- Demonstration of classical trajectories in quantum wave functions.
- Extension of scattering theory to include external fields and multi-particle detectors.

## Abstract

Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from sources at macroscopic distance and measured at macroscopic distance from the microscopic reaction volume. Standard experimental procedure is to describe asymptotic particle motion by classical mechanics. However, this transition to classical mechanics is not accounted for in standard quantum scattering theory. Hence, we revisit conventional scattering theory with the introduction of semiclassical propagators to describe the wave function in both incident and outgoing asymptotic scattering channels. This description leads to the manifestation of classical trajectories in the quantum wave function both before and after the collision. It includes the case of extraction with external fields as in modern multi-particle detectors. We derive the asymptotic Kemble imaging theorem (IT) limit to demonstrate how formal quantum scattering theory contains implicit classical mechanics threaded throughout the asymptotic wave functions.