  In this letter, we calculate the probability for resonantly induced
transitions in quantum states due to time dependent gravitational
perturbations. Contrary to common wisdom, the probability of inducing
transitions is not infinitesimally small. We consider a system of ultra cold
neutrons (UCN), which are organized according to the energy levels of the
Schr\"odinger equation in the presence of the earth's gravitational field.
Transitions between energy levels are induced by an oscillating driving force
of frequency $\omega$. The driving force is created by oscillating a
macroscopic mass in the neighbourhood of the system of neutrons. The neutrons
decay in 880 seconds while the probability of transitions increase as $t^2$.
Hence the optimal strategy is to drive the system for 2 lifetimes. The
transition amplitude then is of the order of $1.06\times 10^{-5}$ hence with a
million ultra cold neutrons, one should be able to observe transitions.
