  In two-dimensional noncommutive space for the case of both position-position
and momentum-momentum noncommuting, the constraint between noncommutative
parameters on the quantum gravitational well is investigated. The related topic
of guaranteeing Bose-Einstein statistics in the general case are elucidated:
Bose-Einstein statistics is guaranteed by the deformed Heisenberg-Weyl algebra
itself, independent of dynamics. A special feature of a dynamical system is
represented by a constraint between noncommutative parameters. Such a
constraint is fixed by dynamical considerations. The general feature of the
constraint is a direct proportionality between noncommutative parameters with a
coefficient composed by a product of characteristic parameters of the
considered system. The constraint on the quantum gravitational well is
obtained, and is applied to estimate the upper bound of the momentum-momentum
noncommutative parameter from the experimental upper bound of the
position-position noncommutative parameter.
