Equivalence between free and harmonically trapped quantum particles
Quantum Physics
2010-08-25 v1 Atomic Physics
Computational Physics
Abstract
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden transition to a harmonic potential can be described by a simple coordinate transformation applied at the transition time. This procedure is computationally more efficient than either state-projection or propagator techniques. A concatenation of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant.
Cite
@article{arxiv.1008.3929,
title = {Equivalence between free and harmonically trapped quantum particles},
author = {Ole Steuernagel},
journal= {arXiv preprint arXiv:1008.3929},
year = {2010}
}
Comments
3 pages, 2 figures