Liouville transformations and quantum reflection
Quantum Physics
2015-06-30 v1
Abstract
Liouville transformations of Schr\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows one to map the problem of quantum reflection of an atom on an attractive Casimir-Polder well into that of reflection on a repulsive wall. We deduce a quantitative evaluation of quantum reflection probabilities in terms of the universal probability which corresponds to the solution of the far-end Casimir-Polder potential.
Keywords
Cite
@article{arxiv.1502.06119,
title = {Liouville transformations and quantum reflection},
author = {Gabriel Dufour and Romain Guérout and Astrid Lambrecht and Serge Reynaud},
journal= {arXiv preprint arXiv:1502.06119},
year = {2015}
}