Scaling of variables and the relation between noncommutative parameters in noncommutative quantum mechanics

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra, invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.