  Gravity is the most familiar force at our natural length scale. However, it
is still exotic from the view point of particle physics. The first experimental
study of quantum effects under gravity was performed using a cold neutron beam
in 1975. Following this, an investigation of gravitationally bound quantum
states using ultracold neutrons was started in 2002. This quantum bound system
is now well understood, and one can use it as a tunable tool to probe gravity.
In this paper, we review a recent measurement of position-space wave functions
of such gravitationally bound states, and discuss issues related to this
analysis, such as neutron loss models in a thin neutron guide, the formulation
of phase space quantum mechanics, and UCN position sensitive detectors. The
quantum modulation of neutron bound states measured in this experiment shows
good agreement with the prediction from quantum mechanics.
