Evolution of the wave-function's shape in a time-dependent harmonic potential
Abstract
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave-packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave-function. We review how to extract the effective dynamics for Gaussian wave-packets evolving according to the Schrodinger equation with time-dependent potential in a 1+1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave-function in a time-dependent harmonic potential.
Cite
@article{arxiv.2305.03847,
title = {Evolution of the wave-function's shape in a time-dependent harmonic potential},
author = {Etera R. Livine},
journal= {arXiv preprint arXiv:2305.03847},
year = {2023}
}
Comments
7 pages, v3: accepted for publication by EPL