The main goal of this diploma thesis war the supervision and implementation of a set up for a neutron spectrometer. This spectrometer is part of the qBounce experiment and was designed with the neutron an quantum physics group at the ATI in Vienna. The spectrometer itself is located at the UCN beam line PF2 of the ILL. The goal was to perform Ramsey spectroscopic measurements using UCNs bound in the Earths gravitational field for the first time.