QUANTUM TRANSFORMATIONS

We show that the stationary quantum Hamilton-Jacobi equation of nonrelativistic 1D systems, underlying Bohmian mechanics, takes the classical form with ∂q replaced by ∂q where dq=dq/sqrt(1-β2). The β2 term essentially 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, these ``quantum transformations'' indicate that the classical and quantum potentials deform space geometry.