  A planar phase space having both position and momentum noncommutativity is
defined in a more inclusive setting than that considered elsewhere. The
dynamics of a particle in a gravitational quantum well in this space is
studied. The use of the WKB approximation and the virial theorem enable
analytic discussions on the effect of noncommutativity. Consistent results are
obtained following either commutative space or noncommutative space
descriptions. Comparison with recent experimental data with cold neutrons at
Grenoble imposes an upper bound on the noncommutative parameter. Also, our
results are compared with a recent numerical analysis of a similar problem.
