  In the paper by V.V. Nesvizhevsky et al., Phys. Rev. D 67, 102002 (2003), it
is argued that the lowest quantum state of neutrons in the Earth's
gravitational field has been experimentally identified. While this is most
likely correct, it is imperative to investigate all alternative explanations of
the result in order to close all loopholes, as it is the first experiment ever
claimed to have observed gravitational quantum states. Here we show that
geometrical effects in the experimental setup can mimic the results attributed
to gravity. Modifications of the experimental setup to close these possible
loopholes are suggested.
