  Previous studies of gravitationally bound states of ultracold neutrons showed
the quantization of energy levels, and confirmed quantum mechanical predictions
for the average size of the two lowest energy states wave functions.
Improvements in position-like measurements can increase the accuracy by an
order of magnitude only. We therefore develop another approach, consisting in
accurate measurements of the energy levels. The GRANIT experiment is devoted to
the study of resonant transitions between quantum states induced by an
oscillating perturbation.
  According to Heisenberg's uncertainty relations, the accuracy of measurement
of the energy levels is limited by the time available to perform the
transitions. Thus, trapping quantum states will be necessary, and each source
of losses has to be controlled in order to maximize the lifetime of the states.
We discuss the general principles of transitions between quantum states, and
consider the main systematical losses of neutrons in a trap.
