  We propose a theoretical analysis of the experimental data by Ichikawa et al.
(Phys. Rev. Lett. 112, 071101 (2014)) on a spatial distribution of ultracold
neutrons in the gravitational field of the Earth above a mirror, projected onto
a pixelated detector by scattering by a cylindrical mirror. We calculate a
theoretical spatial distribution of a probability density of quantum
gravitational states of ultracold neutrons and analyse a spatial distribution
of quantum gravitational states in term of the Wigner function. We cannot
confirm that the experimental data by Ichikawa et al. (Phys. Rev. Lett. 112,
071101 (2014)) correspond to a spatial distribution of quantum gravitational
states of ultracold neutrons.
