The Particle in the box: Intermode traces in the propagator

TL;DR

This paper reveals that intermode traces, characteristic structures in the probability distribution of a particle in a box, are inherently present in the propagator and depend on the initial wave packet's factorization.

Contribution

It demonstrates that intermode traces are embedded in the propagator itself and links their visibility to the initial wave packet's factorization property.

Findings

Intermode traces are present in the propagator.

Visibility of structures depends on initial wave packet factorization.

Provides insight into the spacetime structure of quantum particles in a box.

Abstract

Characteristic structures such as canals and ridges --intermode traces-- emerge in the spacetime representation of the probability distribution of a particle in a one-dimensional box. We show that the corresponding propagator already contains these structures. We relate their visibility to the factorization property of the initial wave packet.