Quantum versus classical quenches and the broadening of wave packets

TL;DR

This paper compares quantum and classical dynamics following potential quenches, focusing on wave packet broadening, with analytical solutions for harmonic oscillators and insights into Wigner functions.

Contribution

It provides analytical results for quantum quenches in harmonic oscillators and introduces the Wigner function to understand wave packet dynamics.

Findings

Analytical solutions for quantum quenches in harmonic oscillators.

Comparison between quantum and classical wave packet evolution.

Highlighting the unique broadening of Gaussian wave packets.

Abstract

The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks.