  Ultracold neutrons (UCNs) can be bound by the potential of terrestrial
gravity and a reflecting mirror. The wave function of the bound state has
characteristic modulations. We carried out an experiment to observe the
vertical distribution of the UCNs above such a mirror at Institut Laue-Langevin
in 2011. The observed modulation is in good agreement with that prediction by
quantum mechanics using the Wigner function. The spatial resolution of the
detector system is estimated to be 0.7 micro meter. This is the first
observation of gravitationally bound states of UCNs with submicron spatial
resolution.
