  Recently we showed that the postulated diffeomorphic equivalence of states
implies quantum mechanics. This approach takes the canonical variables to be
dependent by the relation p=\partial_q S_0 and exploits a basic
GL(2,C)-symmetry which underlies the canonical formalism. In particular, we
looked for the special transformations leading to the free system with
vanishing energy. Furthermore, we saw that while on the one hand the
equivalence principle cannot be consistently implemented in classical
mechanics, on the other it naturally led to the quantum analogue of the
Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this
letter we show that actually the principle uniquely leads to this solution.
Furthermore, we find the map reducing any system to the free one with vanishing
energy and derive the transformations on S_0 leaving the wave function
invariant. We also express the canonical and Schroedinger equations by means of
the brackets recently introduced in the framework of N=2 SYM. These brackets
are the analogue of the Poisson brackets with the canonical variables taken as
dependent.
