Quantum mechanics from an equivalence principle

We postulate that physical starts are equivalent under coordinate transform ations. We then implement this equivalence principle first in the case of o ne-dimensional stationary systems showing that it leads to the quantum anal ogue of the Hamilton-Jacobi equation which in turn implies the Schrodinger equation. In this context the Planck constant plays: the role of covarianti zing parameter. The construction is deeply related to the GL(2,C)-symmetry of the second-order differential equation associated to the Legendre transf ormation which selects, in the case of the quantum analogue of the Hamilton ian characteristic function, self-dual states which guarantee its existence for any physical system. The universal nature of the self-dual states impl ies the Schrodinger equation in any dimension. (C) 1999 Published by Elsevi er Science B.V. All rights reserved.