  In this paper we study the symmetry known as mechanical similarity (LMS) and
present for any monomial potential. We analyze it in the framework of the
Koopman-von Neumann formulation of classical mechanics and prove that in this
framework the LMS can be given a canonical implementation. We also show that
the LMS is a generalization of the scale symmetry which is present only for the
inverse square potential. Finally we study the main obstructions which one
encounters in implementing the LMS at the quantum mechanical level.
