A quantum mechanical description of the experiment on the observation of gravitationally bound states

Quantum states in the earth's gravitational field have been observed, with ultra-cold neutrons falling under gravity. The experimental results can be described by the quantum mechanical scattering model 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 quantitatively describes, particularly, the experimentally realized situation of reversed gravity, we can practically rule out alternative explanations of the quantum states, in terms of pure confinement effects.