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 (13)

• 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
• Exactly solvable Schrödinger operators
• 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
• Shaping the distribution of vertical velocities of antihydrogen in GBAR
• Quantum reflection and Liouville transformations from wells to walls

Cited by in corpus (4)

• 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
• Improved Effective Range Expansion for Casimir-Polder potential