Liouville transformations and quantum reflection

Abstract

Liouville transformations of Schrödinger 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 $V_4=-C_4/z^4$ far-end Casimir-Polder potential.

References in corpus (5)

• Low velocity quantum reflection of Bose-Einstein condensates
• The Casimir force and the quantum theory of lossy optical cavities
• Interaction of Ultracold Antihydrogen with a Conducting Wall
• Coherent reflection of He atom beams from rough surfaces at near-grazing incidence
• Quantum reflection and Liouville transformations from wells to walls