Study of the neutron quantum states in the gravity field
  We have studied neutron quantum states in the potential well formed by the earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of ~2 microns was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment. 
V.V.Nesvizhevsky, A.K.Petukhov, H.G.Boerner, T.A.Baranova,   A.M.Gagarski, G.A.Petrov, K.V.Protasov, A.Yu.Voronin, S.Baessle...