Quantum reflection and Liouville transformations from wells to walls
Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, Campus Jussieu - F-75252 Paris, France
Received: 19 February 2015
Accepted: 6 May 2015
Liouville transformations map in a rigorous manner one Schrödinger equation into another, with a changed scattering potential. They are used here to transform quantum reflection of an atom on an attractive Casimir-Polder well into reflection of the atom on a repulsive wall. While the scattering properties are preserved, the corresponding semiclassical descriptions are completely different. A quantitative evaluation of quantum reflection probabilities is deduced from this method.
PACS: 03.65.-w – Quantum mechanics / 34.35.+a – Interactions of atoms and molecules with surfaces / 02.30.Hq – Ordinary differential equations
© EPLA, 2015