A quantum mechanical description of the experiment on the observation of   gravitationally bound states
  Quantum states in the Earth's gravitational field were observed, when ultra-cold neutrons fall under gravity. The experimental results can be described by the quantum mechanical scattering model as it is presented here. We also discuss other geometries of the experimental setup which correspond to the absence or the reversion of gravity. Since our quantum mechanical model describes, particularly, the experimentally realized situation of reversed gravity quantitatively, we can practically rule out alternative explanations of the quantum states in terms of pure confinement effects. 
Alexander Westphal, H. Abele, S. Baessler, V. V. Nesvizhevsky, A. K.   Petukhov, K. V. Protasov, A. Yu. Voronin