Spatial Distribution of Ultracold Neutron Probability Density in the Gravitational Field of the Earth Above a Mirror

We present a theoretical analysis of the experimental data reported by Ichikawa et al. on the spatial distribution of ultracold neutrons in the Earth’s gravitational field above a mirror. The data involve a projection onto a pixelated detector via scattering by a cylindrical mirror. Our study includes a calculation of the theoretical spatial distribution of the probability density associated with the quantum gravitational states of ultracold neutrons. Furthermore, we analyze this spatial distribution using the Wigner function framework. Based on our analysis, we cannot confirm that the experimental data reported by Ichikawa et al. correspond to the spatial distribution of quantum gravitational states of ultracold neutrons.