QUANTUM TRANSFORMATIONS

We show that the stationary quantum Hamilton-Jacobi equation of nonrel ativistic 1D systems, underlying Bohmian mechanics, takes the classica l form with partial derivative(q) replaced by partial derivative((q) o ver cap) where d (q) over cap = dq/root 1-beta(2). The beta(2) term es sentially coincides with the quantum potential that, like V - E, turns out to be proportional to a curvature arising in projective geometry. In agreement with the recently formulated equivalence principle, thes e ''quantum transformations'' indicate that the classical and quantum potentials deform space geometry. (C) 1998 Elsevier Science B.V.