English

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 V4=C4/z4V_4=-C_4/z^4 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}
}
R2 v1 2026-06-22T08:34:37.579Z