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We propose a theoretical analysis of the experimental data by Ichikawa et al.(Phys. Rev. Lett. 112, 071101 (2014)) on a spatial distribution of ultracoldneutrons in the gravitational field of the Earth above a mirror, projected ontoa pixelated detector by scattering by a cylindrical mirror. We calculate atheoretical spatial distribution of a probability density of quantumgravitational states of ultracold neutrons and analyse a spatial distributionof quantum gravitational states in term of the Wigner function. We cannotconfirm that the experimental data by Ichikawa et al. (Phys. Rev. Lett. 112,071101 (2014)) correspond to a spatial distribution of quantum gravitationalstates of ultracold neutrons.

Spatial distribution of ultracold neutron probability density in the gravitational field of the earth above a mirror