  We show that the stationary quantum Hamilton-Jacobi equation of
non-relativistic 1D systems, underlying Bohmian mechanics, takes the classical
form with $\partial_q$ replaced by $\partial_{\hat q}$ where $d\hat q={dq\over
\sqrt{1-\beta^2}}$. The $\beta^2$ 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.
