# Classical hallmarks of macroscopic quantum wave function propagation

## TL;DR

This paper demonstrates that the imaging theorem (IT) based on the semiclassical propagator provides a precise link between quantum wave functions and classical trajectories, allowing wave functions to be preserved at macroscopic distances with classical variables.

## Contribution

It introduces the imaging theorem as an alternative to standard scattering theory for connecting quantum wave functions with classical trajectories.

## Key findings

- Wave functions are preserved over macroscopic distances.
- Variables of wave functions describe classical trajectories.
- IT offers a time-dependent approach for experimental comparison.

## Abstract

The precise connection between quantum wave functions and the underlying classical trajectories often is presented rather vaguely by practitioners of quantum mechanics. Here we demonstrate, with simple examples, that the imaging theorem (IT) based on the semiclassical propagator provides a precise connection. Wave functions are preserved out to macroscopic distances but the variables, position and momentum, of these functions describe classical trajectories. We show that the IT, based on an overtly time-dependent picture, provides a strategy alternative to standard scattering theory with which to compare experimental results to theory.