We propose to apply Ramseys method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a vertical mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schrodinger
wave packet bouncing off a hard surface in the gravitational field of the earth. Measurements with ultra-cold neutrons will offer a sensitivity to Newtons law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.
