  We study quantum reflection of antihydrogen atoms from matter slabs due to
the van der Waals/Casimir-Polder (vdW/CP) potential. By taking into account the
specificities of antihydrogen and the optical properties and width of the slabs
we calculate realistic estimates for the potential and quantum reflection
amplitudes. Next we discuss the paradoxical result of larger reflection
coefficients estimated for weaker potentials in terms of the Schwarzian
derivative. We analyze the limiting case of reflections at small energies,
which are characterized by a scattering length and have interesting
applications for trapping and guiding antihydrogen using material walls.
