Bohm potential for the time dependent harmonic oscillator
Quantum Physics
2022-01-12 v1 Mathematical Physics
math.MP
Abstract
In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadratically on position and show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.
Cite
@article{arxiv.2101.05907,
title = {Bohm potential for the time dependent harmonic oscillator},
author = {Francisco Soto-Eguibar and Felipe A. Asenjo and Sergio A. Hojman and Héctor M. Moya-Cessa},
journal= {arXiv preprint arXiv:2101.05907},
year = {2022}
}