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. 
O. Bertolami, J. G. Rosa, C. M. L. de Arag\~ao, P. Castorina, D.   Zappal\`a