  Gravity is the weakest of all four known forces in the universe. Quantum
states of an elementary particle due to such a weak field is certainly very
shallow and would therefore be an experimental challenge to detect. Recently an
experimental attempt was made by V. V. Nesvizhevsky et al., Nature 415, 297
(2002), to measure the quantum states of a neutron, which shows that ground
state and few excited states are \sim 10^{-12}eV. We show that the energy of
the ground state of a neutron confined above Earth's surface should be \sim
10^{-37}eV. The experimentally observed energy levels are 10^{25} times deeper
than the actual energy levels it should be and thus certainly not due to
gravitational effect of Earth. Therefore the correct interpretation for the
painstaking experimental results of Ref. \cite{nes1} is due to the confinement
potential of a one dimensional box of length L \sim 50\mu m, generated from the
experimental setup as commented before \cite{hansoon}. Our results thus creates
a new challenge to the experimentalist to resolve the shallow energy levels of
the neutron in Earth's gravitational field in future.
