  A basic aspect of the recently proposed approach to quantum mechanics is that
no use of any axiomatic interpretation of the wave function is made. In
particular, the quantum potential turns out to be an intrinsic potential energy
of the particle, which, similarly to the relativistic rest energy, is never
vanishing. This is related to the tunnel effect, a consequence of the fact that
the conjugate momentum field is real even in the classically forbidden regions.
The quantum stationary Hamilton-Jacobi equation is defined only if the ratio
psi^D/psi of two real linearly independent solutions of the Schroedinger
equation, and therefore of the trivializing map, is a local homeomorphism of
the extended real line into itself, a consequence of the Moebius symmetry of
the Schwarzian derivative. In this respect we prove a basic theorem relating
the request of continuity at spatial infinity of psi^D/psi, a consequence of
the q - 1/q duality of the Schwarzian derivative, to the existence of L^2(R)
solutions of the corresponding Schroedinger equation. As a result, while in the
conventional approach one needs the Schroedinger equation with the L^2(R)
condition, consequence of the axiomatic interpretation of the wave function,
the equivalence principle by itself implies a dynamical equation that does not
need any assumption and reproduces both the tunnel effect and energy
quantization.
