Structure invariant wave packets

TL;DR

This paper demonstrates that adding a quadratic phase to an initial wavefunction can produce an approximately invariant structure during free evolution, closely matching the exact evolution and revealing new insights into wave packet dynamics.

Contribution

It introduces a method to achieve approximate structure invariance in wave packet evolution by applying a quadratic phase, a novel approach in wave dynamics.

Findings

Invariant structure closely matches exact evolution

Quadratic phase addition effectively controls wave spreading

Method applicable to various initial wavefunctions

Abstract

We show that by adding a quadratic phase to an initial arbitrary wavefunction, its free evolution maintains an invariant structure while it spreads by the action of an squeeze operator. Although such invariance is an approximation, we show that it matches perfectly the exact evolution.