Quantum reflection and Liouville transformations from wells to walls

Abstract

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 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.

References in corpus (11)

• Quantum reflection of atoms from a solid surface at normal incidence
• Experimental Observation of Quantum Reflection in the High Energy Limit
• 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
• Quantum motion of a neutron in a wave-guide in the gravitational field
• Quantum reflection of antihydrogen from Casimir potential above matter slabs
• Quantum-defect theory for $-1/r^4$ type of interactions
• Coherent reflection of He atom beams from rough surfaces at near-grazing incidence
• Quantum reflection of antihydrogen from nanoporous media
• Quantum reflection and Liouville transformations from wells to walls

Cited by in corpus (7)

• Quantum threshold reflection is not a consequence of the badlands region of the potential
• Casimir-Polder shifts on quantum levitation states
• Quantum reflection of antihydrogen from a liquid helium film
• Quantum reflection and Liouville transformations from wells to walls
• Liouville transformations and quantum reflection
• Improved Effective Range Expansion for Casimir-Polder potential
• Quenching of antihydrogen gravitational states by surface charges